Find the Inverse f(x)=4 seventh root of x-8+5

$f (x) = 4 \sqrt[7]{x - 8} + 5$

Write $f (x) = 4 \sqrt[7]{x - 8} + 5$ as an equation.

$y = 4 \sqrt[7]{x - 8} + 5$

Interchange the variables.

$x = 4 \sqrt[7]{y - 8} + 5$

Solve for $y$ .

Rewrite the equation as $4 \sqrt[7]{y - 8} + 5 = x$ .

$4 \sqrt[7]{y - 8} + 5 = x$

Subtract $5$ from both sides of the equation.

$4 \sqrt[7]{y - 8} = x - 5$

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $7$ .

${(4 \sqrt[7]{y - 8})}^{7} = {(x - 5)}^{7}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[7]{y - 8}$ as ${(y - 8)}^{\frac{1}{7}}$ .

${(4 {(y - 8)}^{\frac{1}{7}})}^{7} = {(x - 5)}^{7}$

Simplify the left side.

Simplify ${(4 {(y - 8)}^{\frac{1}{7}})}^{7}$ .

Apply the product rule to $4 {(y - 8)}^{\frac{1}{7}}$ .

$4^{7} {({(y - 8)}^{\frac{1}{7}})}^{7} = {(x - 5)}^{7}$

Raise $4$ to the power of $7$ .

$16384 {({(y - 8)}^{\frac{1}{7}})}^{7} = {(x - 5)}^{7}$

Multiply the exponents in ${({(y - 8)}^{\frac{1}{7}})}^{7}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$16384 {(y - 8)}^{\frac{1}{7} \cdot 7} = {(x - 5)}^{7}$

Cancel the common factor of $7$ .

Cancel the common factor.

$16384 {(y - 8)}^{\frac{1}{7} \cdot 7} = {(x - 5)}^{7}$

Rewrite the expression.

$16384 {(y - 8)}^{1} = {(x - 5)}^{7}$

Simplify.

$16384 (y - 8) = {(x - 5)}^{7}$

Apply the distributive property.

$16384 y + 16384 \cdot - 8 = {(x - 5)}^{7}$

Multiply $16384$ by $- 8$ .

$16384 y - 131072 = {(x - 5)}^{7}$

Simplify the right side.

Simplify ${(x - 5)}^{7}$ .

Use the Binomial Theorem.

$16384 y - 131072 = x^{7} + 7 x^{6} \cdot - 5 + 21 x^{5} {(- 5)}^{2} + 35 x^{4} {(- 5)}^{3} + 35 x^{3} {(- 5)}^{4} + 21 x^{2} {(- 5)}^{5} + 7 x {(- 5)}^{6} + {(- 5)}^{7}$

Simplify each term.

Multiply $- 5$ by $7$ .

$16384 y - 131072 = x^{7} - 35 x^{6} + 21 x^{5} {(- 5)}^{2} + 35 x^{4} {(- 5)}^{3} + 35 x^{3} {(- 5)}^{4} + 21 x^{2} {(- 5)}^{5} + 7 x {(- 5)}^{6} + {(- 5)}^{7}$

Raise $- 5$ to the power of $2$ .

$16384 y - 131072 = x^{7} - 35 x^{6} + 21 x^{5} \cdot 25 + 35 x^{4} {(- 5)}^{3} + 35 x^{3} {(- 5)}^{4} + 21 x^{2} {(- 5)}^{5} + 7 x {(- 5)}^{6} + {(- 5)}^{7}$

Multiply $25$ by $21$ .

$16384 y - 131072 = x^{7} - 35 x^{6} + 525 x^{5} + 35 x^{4} {(- 5)}^{3} + 35 x^{3} {(- 5)}^{4} + 21 x^{2} {(- 5)}^{5} + 7 x {(- 5)}^{6} + {(- 5)}^{7}$

Raise $- 5$ to the power of $3$ .

$16384 y - 131072 = x^{7} - 35 x^{6} + 525 x^{5} + 35 x^{4} \cdot - 125 + 35 x^{3} {(- 5)}^{4} + 21 x^{2} {(- 5)}^{5} + 7 x {(- 5)}^{6} + {(- 5)}^{7}$

Multiply $- 125$ by $35$ .

$16384 y - 131072 = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 35 x^{3} {(- 5)}^{4} + 21 x^{2} {(- 5)}^{5} + 7 x {(- 5)}^{6} + {(- 5)}^{7}$

Raise $- 5$ to the power of $4$ .

$16384 y - 131072 = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 35 x^{3} \cdot 625 + 21 x^{2} {(- 5)}^{5} + 7 x {(- 5)}^{6} + {(- 5)}^{7}$

Multiply $625$ by $35$ .

$16384 y - 131072 = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} + 21 x^{2} {(- 5)}^{5} + 7 x {(- 5)}^{6} + {(- 5)}^{7}$

Raise $- 5$ to the power of $5$ .

$16384 y - 131072 = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} + 21 x^{2} \cdot - 3125 + 7 x {(- 5)}^{6} + {(- 5)}^{7}$

Multiply $- 3125$ by $21$ .

$16384 y - 131072 = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 7 x {(- 5)}^{6} + {(- 5)}^{7}$

Raise $- 5$ to the power of $6$ .

$16384 y - 131072 = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 7 x \cdot 15625 + {(- 5)}^{7}$

Multiply $15625$ by $7$ .

$16384 y - 131072 = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 109375 x + {(- 5)}^{7}$

Raise $- 5$ to the power of $7$ .

$16384 y - 131072 = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 109375 x - 78125$

Solve for $y$ .

Move all terms not containing $y$ to the right side of the equation.

Add $131072$ to both sides of the equation.

$16384 y = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 109375 x - 78125 + 131072$

Add $- 78125$ and $131072$ .

$16384 y = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 109375 x + 52947$

Divide each term in $16384 y = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 109375 x + 52947$ by $16384$ and simplify.

Divide each term in $16384 y = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 109375 x + 52947$ by $16384$ .

$\frac{16384 y}{16384} = \frac{x^{7}}{16384} + \frac{- 35 x^{6}}{16384} + \frac{525 x^{5}}{16384} + \frac{- 4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} + \frac{- 65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947}{16384}$

Simplify the left side.

Cancel the common factor of $16384$ .

Cancel the common factor.

Divide $y$ by $1$ .

$y = \frac{x^{7}}{16384} + \frac{- 35 x^{6}}{16384} + \frac{525 x^{5}}{16384} + \frac{- 4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} + \frac{- 65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947}{16384}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = \frac{x^{7}}{16384} - \frac{(35) x^{6}}{16384} + \frac{525 x^{5}}{16384} + \frac{- 4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} + \frac{- 65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947}{16384}$

Move the negative in front of the fraction.

$y = \frac{x^{7}}{16384} - \frac{35 x^{6}}{16384} + \frac{525 x^{5}}{16384} - \frac{(4375) x^{4}}{16384} + \frac{21875 x^{3}}{16384} + \frac{- 65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947}{16384}$

Move the negative in front of the fraction.

$y = \frac{x^{7}}{16384} - \frac{35 x^{6}}{16384} + \frac{525 x^{5}}{16384} - \frac{4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} - \frac{65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947}{16384}$

Replace $y$ with $f^{- 1} (x)$ to show the final answer.

$f^{- 1} (x) = \frac{x^{7}}{16384} - \frac{35 x^{6}}{16384} + \frac{525 x^{5}}{16384} - \frac{4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} - \frac{65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947}{16384}$

Verify if $f^{- 1} (x) = \frac{x^{7}}{16384} - \frac{35 x^{6}}{16384} + \frac{525 x^{5}}{16384} - \frac{4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} - \frac{65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947}{16384}$ is the inverse of $f (x) = 4 \sqrt[7]{x - 8} + 5$ .

To verify the inverse, check if $f^{- 1} (f (x)) = x$ and $f (f^{- 1} (x)) = x$ .

Evaluate $f^{- 1} (f (x))$ .

Set up the composite result function.

$f^{- 1} (f (x))$

Evaluate $f^{- 1} (4 \sqrt[7]{x - 8} + 5)$ by substituting in the value of $f$ into $f^{- 1}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{{(4 \sqrt[7]{x - 8} + 5)}^{7}}{16384} - \frac{35 {(4 \sqrt[7]{x - 8} + 5)}^{6}}{16384} + \frac{525 {(4 \sqrt[7]{x - 8} + 5)}^{5}}{16384} - \frac{4375 {(4 \sqrt[7]{x - 8} + 5)}^{4}}{16384} + \frac{21875 {(4 \sqrt[7]{x - 8} + 5)}^{3}}{16384} - \frac{65625 {(4 \sqrt[7]{x - 8} + 5)}^{2}}{16384} + \frac{109375 (4 \sqrt[7]{x - 8} + 5)}{16384} + \frac{52947}{16384}$

Combine the numerators over the common denominator.

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{{(4 \sqrt[7]{x - 8} + 5)}^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Simplify each term.

Use the Binomial Theorem.

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{{(4 \sqrt[7]{x - 8})}^{7} + 7 {(4 \sqrt[7]{x - 8})}^{6} \cdot 5 + 21 {(4 \sqrt[7]{x - 8})}^{5} \cdot 5^{2} + 35 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Simplify each term.

Apply the product rule to $4 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{4^{7} {\sqrt[7]{x - 8}}^{7} + 7 {(4 \sqrt[7]{x - 8})}^{6} \cdot 5 + 21 {(4 \sqrt[7]{x - 8})}^{5} \cdot 5^{2} + 35 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $4$ to the power of $7$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 {\sqrt[7]{x - 8}}^{7} + 7 {(4 \sqrt[7]{x - 8})}^{6} \cdot 5 + 21 {(4 \sqrt[7]{x - 8})}^{5} \cdot 5^{2} + 35 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Rewrite ${\sqrt[7]{x - 8}}^{7}$ as $x - 8$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[7]{x - 8}$ as ${(x - 8)}^{\frac{1}{7}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 {({(x - 8)}^{\frac{1}{7}})}^{7} + 7 {(4 \sqrt[7]{x - 8})}^{6} \cdot 5 + 21 {(4 \sqrt[7]{x - 8})}^{5} \cdot 5^{2} + 35 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 {(x - 8)}^{\frac{1}{7} \cdot 7} + 7 {(4 \sqrt[7]{x - 8})}^{6} \cdot 5 + 21 {(4 \sqrt[7]{x - 8})}^{5} \cdot 5^{2} + 35 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Combine $\frac{1}{7}$ and $7$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 {(x - 8)}^{\frac{7}{7}} + 7 {(4 \sqrt[7]{x - 8})}^{6} \cdot 5 + 21 {(4 \sqrt[7]{x - 8})}^{5} \cdot 5^{2} + 35 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Cancel the common factor of $7$ .

Cancel the common factor.

Rewrite the expression.

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 (x - 8) + 7 {(4 \sqrt[7]{x - 8})}^{6} \cdot 5 + 21 {(4 \sqrt[7]{x - 8})}^{5} \cdot 5^{2} + 35 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Simplify.

Apply the distributive property.

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x + 16384 \cdot - 8 + 7 {(4 \sqrt[7]{x - 8})}^{6} \cdot 5 + 21 {(4 \sqrt[7]{x - 8})}^{5} \cdot 5^{2} + 35 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $16384$ by $- 8$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 7 {(4 \sqrt[7]{x - 8})}^{6} \cdot 5 + 21 {(4 \sqrt[7]{x - 8})}^{5} \cdot 5^{2} + 35 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Apply the product rule to $4 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 7 (4^{6} {\sqrt[7]{x - 8}}^{6}) \cdot 5 + 21 {(4 \sqrt[7]{x - 8})}^{5} \cdot 5^{2} + 35 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $4$ to the power of $6$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 7 (4096 {\sqrt[7]{x - 8}}^{6}) \cdot 5 + 21 {(4 \sqrt[7]{x - 8})}^{5} \cdot 5^{2} + 35 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Rewrite ${\sqrt[7]{x - 8}}^{6}$ as ${({(x - 8)}^{6})}^{\frac{1}{7}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 7 (4096 \sqrt[7]{{(x - 8)}^{6}}) \cdot 5 + 21 {(4 \sqrt[7]{x - 8})}^{5} \cdot 5^{2} + 35 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $4096$ by $7$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 28672 \sqrt[7]{{(x - 8)}^{6}} \cdot 5 + 21 {(4 \sqrt[7]{x - 8})}^{5} \cdot 5^{2} + 35 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $5$ by $28672$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 21 {(4 \sqrt[7]{x - 8})}^{5} \cdot 5^{2} + 35 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Apply the product rule to $4 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 21 (4^{5} {\sqrt[7]{x - 8}}^{5}) \cdot 5^{2} + 35 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $4$ to the power of $5$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 21 (1024 {\sqrt[7]{x - 8}}^{5}) \cdot 5^{2} + 35 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Rewrite ${\sqrt[7]{x - 8}}^{5}$ as ${({(x - 8)}^{5})}^{\frac{1}{7}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 21 (1024 \sqrt[7]{{(x - 8)}^{5}}) \cdot 5^{2} + 35 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $1024$ by $21$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 21504 \sqrt[7]{{(x - 8)}^{5}} \cdot 5^{2} + 35 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $5$ to the power of $2$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 21504 \sqrt[7]{{(x - 8)}^{5}} \cdot 25 + 35 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $25$ by $21504$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 35 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Apply the product rule to $4 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 35 (4^{4} {\sqrt[7]{x - 8}}^{4}) \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $4$ to the power of $4$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 35 (256 {\sqrt[7]{x - 8}}^{4}) \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Rewrite ${\sqrt[7]{x - 8}}^{4}$ as ${({(x - 8)}^{4})}^{\frac{1}{7}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 35 (256 \sqrt[7]{{(x - 8)}^{4}}) \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $256$ by $35$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8960 \sqrt[7]{{(x - 8)}^{4}} \cdot 5^{3} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $5$ to the power of $3$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8960 \sqrt[7]{{(x - 8)}^{4}} \cdot 125 + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $125$ by $8960$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 35 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Apply the product rule to $4 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 35 (4^{3} {\sqrt[7]{x - 8}}^{3}) \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $4$ to the power of $3$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 35 (64 {\sqrt[7]{x - 8}}^{3}) \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Rewrite ${\sqrt[7]{x - 8}}^{3}$ as ${({(x - 8)}^{3})}^{\frac{1}{7}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 35 (64 \sqrt[7]{{(x - 8)}^{3}}) \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $64$ by $35$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 2240 \sqrt[7]{{(x - 8)}^{3}} \cdot 5^{4} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $5$ to the power of $4$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 2240 \sqrt[7]{{(x - 8)}^{3}} \cdot 625 + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $625$ by $2240$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 21 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Apply the product rule to $4 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 21 (4^{2} {\sqrt[7]{x - 8}}^{2}) \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $4$ to the power of $2$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 21 (16 {\sqrt[7]{x - 8}}^{2}) \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Rewrite ${\sqrt[7]{x - 8}}^{2}$ as ${({(x - 8)}^{2})}^{\frac{1}{7}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 21 (16 \sqrt[7]{{(x - 8)}^{2}}) \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $16$ by $21$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 336 \sqrt[7]{{(x - 8)}^{2}} \cdot 5^{5} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $5$ to the power of $5$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 336 \sqrt[7]{{(x - 8)}^{2}} \cdot 3125 + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $3125$ by $336$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 7 (4 \sqrt[7]{x - 8}) \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $4$ by $7$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 28 \sqrt[7]{x - 8} \cdot 5^{6} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $5$ to the power of $6$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 28 \sqrt[7]{x - 8} \cdot 15625 + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $15625$ by $28$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} + 5^{7} - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $5$ to the power of $7$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 131072 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} + 78125 - 35 {(4 \sqrt[7]{x - 8} + 5)}^{6} + 525 {(4 \sqrt[7]{x - 8} + 5)}^{5} - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Add $- 131072$ and $78125$ .

Use the Binomial Theorem.

Simplify each term.

Apply the product rule to $4 \sqrt[7]{x - 8}$ .

Raise $4$ to the power of $6$ .

Rewrite ${\sqrt[7]{x - 8}}^{6}$ as ${({(x - 8)}^{6})}^{\frac{1}{7}}$ .

Apply the product rule to $4 \sqrt[7]{x - 8}$ .

Raise $4$ to the power of $5$ .

Rewrite ${\sqrt[7]{x - 8}}^{5}$ as ${({(x - 8)}^{5})}^{\frac{1}{7}}$ .

Multiply $1024$ by $6$ .

Multiply $5$ by $6144$ .

Apply the product rule to $4 \sqrt[7]{x - 8}$ .

Raise $4$ to the power of $4$ .

Rewrite ${\sqrt[7]{x - 8}}^{4}$ as ${({(x - 8)}^{4})}^{\frac{1}{7}}$ .

Multiply $256$ by $15$ .

Raise $5$ to the power of $2$ .

Multiply $25$ by $3840$ .

Apply the product rule to $4 \sqrt[7]{x - 8}$ .

Raise $4$ to the power of $3$ .

Rewrite ${\sqrt[7]{x - 8}}^{3}$ as ${({(x - 8)}^{3})}^{\frac{1}{7}}$ .

Multiply $64$ by $20$ .

Raise $5$ to the power of $3$ .

Multiply $125$ by $1280$ .

Apply the product rule to $4 \sqrt[7]{x - 8}$ .

Raise $4$ to the power of $2$ .

Rewrite ${\sqrt[7]{x - 8}}^{2}$ as ${({(x - 8)}^{2})}^{\frac{1}{7}}$ .

Multiply $16$ by $15$ .

Raise $5$ to the power of $4$ .

Multiply $625$ by $240$ .

Multiply $4$ by $6$ .

Raise $5$ to the power of $5$ .

Multiply $3125$ by $24$ .

Raise $5$ to the power of $6$ .

Apply the distributive property.

Simplify.

Multiply $4096$ by $- 35$ .

Multiply $30720$ by $- 35$ .

Multiply $96000$ by $- 35$ .

Multiply $160000$ by $- 35$ .

Multiply $150000$ by $- 35$ .

Multiply $75000$ by $- 35$ .

Multiply $- 35$ by $15625$ .

Use the Binomial Theorem.

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 ({(4 \sqrt[7]{x - 8})}^{5} + 5 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5 + 10 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{2} + 10 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{3} + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Simplify each term.

Apply the product rule to $4 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (4^{5} {\sqrt[7]{x - 8}}^{5} + 5 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5 + 10 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{2} + 10 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{3} + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $4$ to the power of $5$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 {\sqrt[7]{x - 8}}^{5} + 5 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5 + 10 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{2} + 10 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{3} + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Rewrite ${\sqrt[7]{x - 8}}^{5}$ as ${({(x - 8)}^{5})}^{\frac{1}{7}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 5 {(4 \sqrt[7]{x - 8})}^{4} \cdot 5 + 10 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{2} + 10 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{3} + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Apply the product rule to $4 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 5 (4^{4} {\sqrt[7]{x - 8}}^{4}) \cdot 5 + 10 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{2} + 10 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{3} + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $4$ to the power of $4$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 5 (256 {\sqrt[7]{x - 8}}^{4}) \cdot 5 + 10 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{2} + 10 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{3} + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Rewrite ${\sqrt[7]{x - 8}}^{4}$ as ${({(x - 8)}^{4})}^{\frac{1}{7}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 5 (256 \sqrt[7]{{(x - 8)}^{4}}) \cdot 5 + 10 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{2} + 10 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{3} + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $256$ by $5$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 1280 \sqrt[7]{{(x - 8)}^{4}} \cdot 5 + 10 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{2} + 10 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{3} + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $5$ by $1280$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 6400 \sqrt[7]{{(x - 8)}^{4}} + 10 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5^{2} + 10 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{3} + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Apply the product rule to $4 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 6400 \sqrt[7]{{(x - 8)}^{4}} + 10 (4^{3} {\sqrt[7]{x - 8}}^{3}) \cdot 5^{2} + 10 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{3} + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $4$ to the power of $3$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 6400 \sqrt[7]{{(x - 8)}^{4}} + 10 (64 {\sqrt[7]{x - 8}}^{3}) \cdot 5^{2} + 10 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{3} + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Rewrite ${\sqrt[7]{x - 8}}^{3}$ as ${({(x - 8)}^{3})}^{\frac{1}{7}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 6400 \sqrt[7]{{(x - 8)}^{4}} + 10 (64 \sqrt[7]{{(x - 8)}^{3}}) \cdot 5^{2} + 10 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{3} + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $64$ by $10$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 6400 \sqrt[7]{{(x - 8)}^{4}} + 640 \sqrt[7]{{(x - 8)}^{3}} \cdot 5^{2} + 10 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{3} + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $5$ to the power of $2$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 6400 \sqrt[7]{{(x - 8)}^{4}} + 640 \sqrt[7]{{(x - 8)}^{3}} \cdot 25 + 10 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{3} + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $25$ by $640$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 6400 \sqrt[7]{{(x - 8)}^{4}} + 16000 \sqrt[7]{{(x - 8)}^{3}} + 10 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{3} + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Apply the product rule to $4 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 6400 \sqrt[7]{{(x - 8)}^{4}} + 16000 \sqrt[7]{{(x - 8)}^{3}} + 10 (4^{2} {\sqrt[7]{x - 8}}^{2}) \cdot 5^{3} + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $4$ to the power of $2$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 6400 \sqrt[7]{{(x - 8)}^{4}} + 16000 \sqrt[7]{{(x - 8)}^{3}} + 10 (16 {\sqrt[7]{x - 8}}^{2}) \cdot 5^{3} + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Rewrite ${\sqrt[7]{x - 8}}^{2}$ as ${({(x - 8)}^{2})}^{\frac{1}{7}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 6400 \sqrt[7]{{(x - 8)}^{4}} + 16000 \sqrt[7]{{(x - 8)}^{3}} + 10 (16 \sqrt[7]{{(x - 8)}^{2}}) \cdot 5^{3} + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $16$ by $10$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 6400 \sqrt[7]{{(x - 8)}^{4}} + 16000 \sqrt[7]{{(x - 8)}^{3}} + 160 \sqrt[7]{{(x - 8)}^{2}} \cdot 5^{3} + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $5$ to the power of $3$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 6400 \sqrt[7]{{(x - 8)}^{4}} + 16000 \sqrt[7]{{(x - 8)}^{3}} + 160 \sqrt[7]{{(x - 8)}^{2}} \cdot 125 + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $125$ by $160$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 6400 \sqrt[7]{{(x - 8)}^{4}} + 16000 \sqrt[7]{{(x - 8)}^{3}} + 20000 \sqrt[7]{{(x - 8)}^{2}} + 5 (4 \sqrt[7]{x - 8}) \cdot 5^{4} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $5$ by $5^{4}$ by adding the exponents.

Move $5^{4}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 6400 \sqrt[7]{{(x - 8)}^{4}} + 16000 \sqrt[7]{{(x - 8)}^{3}} + 20000 \sqrt[7]{{(x - 8)}^{2}} + 5^{4} \cdot (5 (4 \sqrt[7]{x - 8})) + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $5^{4}$ by $5$ .

Raise $5$ to the power of $1$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 6400 \sqrt[7]{{(x - 8)}^{4}} + 16000 \sqrt[7]{{(x - 8)}^{3}} + 20000 \sqrt[7]{{(x - 8)}^{2}} + 5^{4} \cdot (5 (4 \sqrt[7]{x - 8})) + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 6400 \sqrt[7]{{(x - 8)}^{4}} + 16000 \sqrt[7]{{(x - 8)}^{3}} + 20000 \sqrt[7]{{(x - 8)}^{2}} + 5^{4 + 1} (4 \sqrt[7]{x - 8}) + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Add $4$ and $1$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 6400 \sqrt[7]{{(x - 8)}^{4}} + 16000 \sqrt[7]{{(x - 8)}^{3}} + 20000 \sqrt[7]{{(x - 8)}^{2}} + 5^{5} (4 \sqrt[7]{x - 8}) + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $5$ to the power of $5$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 6400 \sqrt[7]{{(x - 8)}^{4}} + 16000 \sqrt[7]{{(x - 8)}^{3}} + 20000 \sqrt[7]{{(x - 8)}^{2}} + 3125 (4 \sqrt[7]{x - 8}) + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $4$ by $3125$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 6400 \sqrt[7]{{(x - 8)}^{4}} + 16000 \sqrt[7]{{(x - 8)}^{3}} + 20000 \sqrt[7]{{(x - 8)}^{2}} + 12500 \sqrt[7]{x - 8} + 5^{5}) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $5$ to the power of $5$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}} + 6400 \sqrt[7]{{(x - 8)}^{4}} + 16000 \sqrt[7]{{(x - 8)}^{3}} + 20000 \sqrt[7]{{(x - 8)}^{2}} + 12500 \sqrt[7]{x - 8} + 3125) - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Apply the distributive property.

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 525 (1024 \sqrt[7]{{(x - 8)}^{5}}) + 525 (6400 \sqrt[7]{{(x - 8)}^{4}}) + 525 (16000 \sqrt[7]{{(x - 8)}^{3}}) + 525 (20000 \sqrt[7]{{(x - 8)}^{2}}) + 525 (12500 \sqrt[7]{x - 8}) + 525 \cdot 3125 - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Simplify.

Multiply $1024$ by $525$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 525 (6400 \sqrt[7]{{(x - 8)}^{4}}) + 525 (16000 \sqrt[7]{{(x - 8)}^{3}}) + 525 (20000 \sqrt[7]{{(x - 8)}^{2}}) + 525 (12500 \sqrt[7]{x - 8}) + 525 \cdot 3125 - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $6400$ by $525$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 525 (16000 \sqrt[7]{{(x - 8)}^{3}}) + 525 (20000 \sqrt[7]{{(x - 8)}^{2}}) + 525 (12500 \sqrt[7]{x - 8}) + 525 \cdot 3125 - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $16000$ by $525$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 525 (20000 \sqrt[7]{{(x - 8)}^{2}}) + 525 (12500 \sqrt[7]{x - 8}) + 525 \cdot 3125 - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $20000$ by $525$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 525 (12500 \sqrt[7]{x - 8}) + 525 \cdot 3125 - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $12500$ by $525$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 525 \cdot 3125 - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $525$ by $3125$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 {(4 \sqrt[7]{x - 8} + 5)}^{4} + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Use the Binomial Theorem.

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 ({(4 \sqrt[7]{x - 8})}^{4} + 4 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5 + 6 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{2} + 4 (4 \sqrt[7]{x - 8}) \cdot 5^{3} + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Simplify each term.

Apply the product rule to $4 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (4^{4} {\sqrt[7]{x - 8}}^{4} + 4 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5 + 6 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{2} + 4 (4 \sqrt[7]{x - 8}) \cdot 5^{3} + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $4$ to the power of $4$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 {\sqrt[7]{x - 8}}^{4} + 4 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5 + 6 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{2} + 4 (4 \sqrt[7]{x - 8}) \cdot 5^{3} + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Rewrite ${\sqrt[7]{x - 8}}^{4}$ as ${({(x - 8)}^{4})}^{\frac{1}{7}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 \sqrt[7]{{(x - 8)}^{4}} + 4 {(4 \sqrt[7]{x - 8})}^{3} \cdot 5 + 6 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{2} + 4 (4 \sqrt[7]{x - 8}) \cdot 5^{3} + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Apply the product rule to $4 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 \sqrt[7]{{(x - 8)}^{4}} + 4 (4^{3} {\sqrt[7]{x - 8}}^{3}) \cdot 5 + 6 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{2} + 4 (4 \sqrt[7]{x - 8}) \cdot 5^{3} + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $4$ by $4^{3}$ by adding the exponents.

Move $4^{3}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 \sqrt[7]{{(x - 8)}^{4}} + 4^{3} \cdot (4 {\sqrt[7]{x - 8}}^{3}) \cdot 5 + 6 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{2} + 4 (4 \sqrt[7]{x - 8}) \cdot 5^{3} + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $4^{3}$ by $4$ .

Raise $4$ to the power of $1$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 \sqrt[7]{{(x - 8)}^{4}} + 4^{3} \cdot (4 {\sqrt[7]{x - 8}}^{3}) \cdot 5 + 6 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{2} + 4 (4 \sqrt[7]{x - 8}) \cdot 5^{3} + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 \sqrt[7]{{(x - 8)}^{4}} + 4^{3 + 1} {\sqrt[7]{x - 8}}^{3} \cdot 5 + 6 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{2} + 4 (4 \sqrt[7]{x - 8}) \cdot 5^{3} + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Add $3$ and $1$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 \sqrt[7]{{(x - 8)}^{4}} + 4^{4} {\sqrt[7]{x - 8}}^{3} \cdot 5 + 6 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{2} + 4 (4 \sqrt[7]{x - 8}) \cdot 5^{3} + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $4$ to the power of $4$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 \sqrt[7]{{(x - 8)}^{4}} + 256 {\sqrt[7]{x - 8}}^{3} \cdot 5 + 6 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{2} + 4 (4 \sqrt[7]{x - 8}) \cdot 5^{3} + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Rewrite ${\sqrt[7]{x - 8}}^{3}$ as ${({(x - 8)}^{3})}^{\frac{1}{7}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 \sqrt[7]{{(x - 8)}^{4}} + 256 \sqrt[7]{{(x - 8)}^{3}} \cdot 5 + 6 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{2} + 4 (4 \sqrt[7]{x - 8}) \cdot 5^{3} + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $5$ by $256$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 \sqrt[7]{{(x - 8)}^{4}} + 1280 \sqrt[7]{{(x - 8)}^{3}} + 6 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5^{2} + 4 (4 \sqrt[7]{x - 8}) \cdot 5^{3} + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Apply the product rule to $4 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 \sqrt[7]{{(x - 8)}^{4}} + 1280 \sqrt[7]{{(x - 8)}^{3}} + 6 (4^{2} {\sqrt[7]{x - 8}}^{2}) \cdot 5^{2} + 4 (4 \sqrt[7]{x - 8}) \cdot 5^{3} + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $4$ to the power of $2$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 \sqrt[7]{{(x - 8)}^{4}} + 1280 \sqrt[7]{{(x - 8)}^{3}} + 6 (16 {\sqrt[7]{x - 8}}^{2}) \cdot 5^{2} + 4 (4 \sqrt[7]{x - 8}) \cdot 5^{3} + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Rewrite ${\sqrt[7]{x - 8}}^{2}$ as ${({(x - 8)}^{2})}^{\frac{1}{7}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 \sqrt[7]{{(x - 8)}^{4}} + 1280 \sqrt[7]{{(x - 8)}^{3}} + 6 (16 \sqrt[7]{{(x - 8)}^{2}}) \cdot 5^{2} + 4 (4 \sqrt[7]{x - 8}) \cdot 5^{3} + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $16$ by $6$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 \sqrt[7]{{(x - 8)}^{4}} + 1280 \sqrt[7]{{(x - 8)}^{3}} + 96 \sqrt[7]{{(x - 8)}^{2}} \cdot 5^{2} + 4 (4 \sqrt[7]{x - 8}) \cdot 5^{3} + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $5$ to the power of $2$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 \sqrt[7]{{(x - 8)}^{4}} + 1280 \sqrt[7]{{(x - 8)}^{3}} + 96 \sqrt[7]{{(x - 8)}^{2}} \cdot 25 + 4 (4 \sqrt[7]{x - 8}) \cdot 5^{3} + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $25$ by $96$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 \sqrt[7]{{(x - 8)}^{4}} + 1280 \sqrt[7]{{(x - 8)}^{3}} + 2400 \sqrt[7]{{(x - 8)}^{2}} + 4 (4 \sqrt[7]{x - 8}) \cdot 5^{3} + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $4$ by $4$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 \sqrt[7]{{(x - 8)}^{4}} + 1280 \sqrt[7]{{(x - 8)}^{3}} + 2400 \sqrt[7]{{(x - 8)}^{2}} + 16 \sqrt[7]{x - 8} \cdot 5^{3} + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $5$ to the power of $3$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 \sqrt[7]{{(x - 8)}^{4}} + 1280 \sqrt[7]{{(x - 8)}^{3}} + 2400 \sqrt[7]{{(x - 8)}^{2}} + 16 \sqrt[7]{x - 8} \cdot 125 + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $125$ by $16$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 \sqrt[7]{{(x - 8)}^{4}} + 1280 \sqrt[7]{{(x - 8)}^{3}} + 2400 \sqrt[7]{{(x - 8)}^{2}} + 2000 \sqrt[7]{x - 8} + 5^{4}) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $5$ to the power of $4$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 \sqrt[7]{{(x - 8)}^{4}} + 1280 \sqrt[7]{{(x - 8)}^{3}} + 2400 \sqrt[7]{{(x - 8)}^{2}} + 2000 \sqrt[7]{x - 8} + 625) + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Apply the distributive property.

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 4375 (256 \sqrt[7]{{(x - 8)}^{4}}) - 4375 (1280 \sqrt[7]{{(x - 8)}^{3}}) - 4375 (2400 \sqrt[7]{{(x - 8)}^{2}}) - 4375 (2000 \sqrt[7]{x - 8}) - 4375 \cdot 625 + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Simplify.

Multiply $256$ by $- 4375$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 4375 (1280 \sqrt[7]{{(x - 8)}^{3}}) - 4375 (2400 \sqrt[7]{{(x - 8)}^{2}}) - 4375 (2000 \sqrt[7]{x - 8}) - 4375 \cdot 625 + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $1280$ by $- 4375$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 4375 (2400 \sqrt[7]{{(x - 8)}^{2}}) - 4375 (2000 \sqrt[7]{x - 8}) - 4375 \cdot 625 + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $2400$ by $- 4375$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 4375 (2000 \sqrt[7]{x - 8}) - 4375 \cdot 625 + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $2000$ by $- 4375$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 4375 \cdot 625 + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $- 4375$ by $625$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 21875 {(4 \sqrt[7]{x - 8} + 5)}^{3} - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Use the Binomial Theorem.

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 21875 ({(4 \sqrt[7]{x - 8})}^{3} + 3 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5 + 3 (4 \sqrt[7]{x - 8}) \cdot 5^{2} + 5^{3}) - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Simplify each term.

Apply the product rule to $4 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 21875 (4^{3} {\sqrt[7]{x - 8}}^{3} + 3 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5 + 3 (4 \sqrt[7]{x - 8}) \cdot 5^{2} + 5^{3}) - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $4$ to the power of $3$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 21875 (64 {\sqrt[7]{x - 8}}^{3} + 3 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5 + 3 (4 \sqrt[7]{x - 8}) \cdot 5^{2} + 5^{3}) - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Rewrite ${\sqrt[7]{x - 8}}^{3}$ as ${({(x - 8)}^{3})}^{\frac{1}{7}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 21875 (64 \sqrt[7]{{(x - 8)}^{3}} + 3 {(4 \sqrt[7]{x - 8})}^{2} \cdot 5 + 3 (4 \sqrt[7]{x - 8}) \cdot 5^{2} + 5^{3}) - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Apply the product rule to $4 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 21875 (64 \sqrt[7]{{(x - 8)}^{3}} + 3 (4^{2} {\sqrt[7]{x - 8}}^{2}) \cdot 5 + 3 (4 \sqrt[7]{x - 8}) \cdot 5^{2} + 5^{3}) - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $4$ to the power of $2$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 21875 (64 \sqrt[7]{{(x - 8)}^{3}} + 3 (16 {\sqrt[7]{x - 8}}^{2}) \cdot 5 + 3 (4 \sqrt[7]{x - 8}) \cdot 5^{2} + 5^{3}) - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Rewrite ${\sqrt[7]{x - 8}}^{2}$ as ${({(x - 8)}^{2})}^{\frac{1}{7}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 21875 (64 \sqrt[7]{{(x - 8)}^{3}} + 3 (16 \sqrt[7]{{(x - 8)}^{2}}) \cdot 5 + 3 (4 \sqrt[7]{x - 8}) \cdot 5^{2} + 5^{3}) - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $16$ by $3$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 21875 (64 \sqrt[7]{{(x - 8)}^{3}} + 48 \sqrt[7]{{(x - 8)}^{2}} \cdot 5 + 3 (4 \sqrt[7]{x - 8}) \cdot 5^{2} + 5^{3}) - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $5$ by $48$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 21875 (64 \sqrt[7]{{(x - 8)}^{3}} + 240 \sqrt[7]{{(x - 8)}^{2}} + 3 (4 \sqrt[7]{x - 8}) \cdot 5^{2} + 5^{3}) - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $4$ by $3$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 21875 (64 \sqrt[7]{{(x - 8)}^{3}} + 240 \sqrt[7]{{(x - 8)}^{2}} + 12 \sqrt[7]{x - 8} \cdot 5^{2} + 5^{3}) - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $5$ to the power of $2$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 21875 (64 \sqrt[7]{{(x - 8)}^{3}} + 240 \sqrt[7]{{(x - 8)}^{2}} + 12 \sqrt[7]{x - 8} \cdot 25 + 5^{3}) - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $25$ by $12$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 21875 (64 \sqrt[7]{{(x - 8)}^{3}} + 240 \sqrt[7]{{(x - 8)}^{2}} + 300 \sqrt[7]{x - 8} + 5^{3}) - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $5$ to the power of $3$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 21875 (64 \sqrt[7]{{(x - 8)}^{3}} + 240 \sqrt[7]{{(x - 8)}^{2}} + 300 \sqrt[7]{x - 8} + 125) - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Apply the distributive property.

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 21875 (64 \sqrt[7]{{(x - 8)}^{3}}) + 21875 (240 \sqrt[7]{{(x - 8)}^{2}}) + 21875 (300 \sqrt[7]{x - 8}) + 21875 \cdot 125 - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Simplify.

Multiply $64$ by $21875$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 21875 (240 \sqrt[7]{{(x - 8)}^{2}}) + 21875 (300 \sqrt[7]{x - 8}) + 21875 \cdot 125 - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $240$ by $21875$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 21875 (300 \sqrt[7]{x - 8}) + 21875 \cdot 125 - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $300$ by $21875$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 21875 \cdot 125 - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $21875$ by $125$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 65625 {(4 \sqrt[7]{x - 8} + 5)}^{2} + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Rewrite ${(4 \sqrt[7]{x - 8} + 5)}^{2}$ as $(4 \sqrt[7]{x - 8} + 5) (4 \sqrt[7]{x - 8} + 5)$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 65625 ((4 \sqrt[7]{x - 8} + 5) (4 \sqrt[7]{x - 8} + 5)) + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Expand $(4 \sqrt[7]{x - 8} + 5) (4 \sqrt[7]{x - 8} + 5)$ using the FOIL Method.

Apply the distributive property.

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 65625 (4 \sqrt[7]{x - 8} (4 \sqrt[7]{x - 8} + 5) + 5 (4 \sqrt[7]{x - 8} + 5)) + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Apply the distributive property.

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 65625 (4 \sqrt[7]{x - 8} (4 \sqrt[7]{x - 8}) + 4 \sqrt[7]{x - 8} \cdot 5 + 5 (4 \sqrt[7]{x - 8} + 5)) + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Apply the distributive property.

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 65625 (4 \sqrt[7]{x - 8} (4 \sqrt[7]{x - 8}) + 4 \sqrt[7]{x - 8} \cdot 5 + 5 (4 \sqrt[7]{x - 8}) + 5 \cdot 5) + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Simplify and combine like terms.

Simplify each term.

Multiply $4 \sqrt[7]{x - 8} (4 \sqrt[7]{x - 8})$ .

Multiply $4$ by $4$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 65625 (16 \sqrt[7]{x - 8} \sqrt[7]{x - 8} + 4 \sqrt[7]{x - 8} \cdot 5 + 5 (4 \sqrt[7]{x - 8}) + 5 \cdot 5) + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $\sqrt[7]{x - 8}$ to the power of $1$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 65625 (16 (\sqrt[7]{x - 8} \sqrt[7]{x - 8}) + 4 \sqrt[7]{x - 8} \cdot 5 + 5 (4 \sqrt[7]{x - 8}) + 5 \cdot 5) + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Raise $\sqrt[7]{x - 8}$ to the power of $1$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 65625 (16 (\sqrt[7]{x - 8} \sqrt[7]{x - 8}) + 4 \sqrt[7]{x - 8} \cdot 5 + 5 (4 \sqrt[7]{x - 8}) + 5 \cdot 5) + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 65625 (16 {\sqrt[7]{x - 8}}^{1 + 1} + 4 \sqrt[7]{x - 8} \cdot 5 + 5 (4 \sqrt[7]{x - 8}) + 5 \cdot 5) + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Add $1$ and $1$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 65625 (16 {\sqrt[7]{x - 8}}^{2} + 4 \sqrt[7]{x - 8} \cdot 5 + 5 (4 \sqrt[7]{x - 8}) + 5 \cdot 5) + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Rewrite ${\sqrt[7]{x - 8}}^{2}$ as ${({(x - 8)}^{2})}^{\frac{1}{7}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 65625 (16 \sqrt[7]{{(x - 8)}^{2}} + 4 \sqrt[7]{x - 8} \cdot 5 + 5 (4 \sqrt[7]{x - 8}) + 5 \cdot 5) + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $5$ by $4$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 65625 (16 \sqrt[7]{{(x - 8)}^{2}} + 20 \sqrt[7]{x - 8} + 5 (4 \sqrt[7]{x - 8}) + 5 \cdot 5) + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $4$ by $5$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 65625 (16 \sqrt[7]{{(x - 8)}^{2}} + 20 \sqrt[7]{x - 8} + 20 \sqrt[7]{x - 8} + 5 \cdot 5) + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $5$ by $5$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 65625 (16 \sqrt[7]{{(x - 8)}^{2}} + 20 \sqrt[7]{x - 8} + 20 \sqrt[7]{x - 8} + 25) + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Add $20 \sqrt[7]{x - 8}$ and $20 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 65625 (16 \sqrt[7]{{(x - 8)}^{2}} + 40 \sqrt[7]{x - 8} + 25) + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Apply the distributive property.

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 65625 (16 \sqrt[7]{{(x - 8)}^{2}}) - 65625 (40 \sqrt[7]{x - 8}) - 65625 \cdot 25 + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Simplify.

Multiply $16$ by $- 65625$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 1050000 \sqrt[7]{{(x - 8)}^{2}} - 65625 (40 \sqrt[7]{x - 8}) - 65625 \cdot 25 + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $40$ by $- 65625$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 1050000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 65625 \cdot 25 + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Multiply $- 65625$ by $25$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 1050000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 1640625 + 109375 (4 \sqrt[7]{x - 8} + 5) + 52947}{16384}$

Apply the distributive property.

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 1050000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 1640625 + 109375 (4 \sqrt[7]{x - 8}) + 109375 \cdot 5 + 52947}{16384}$

Multiply $4$ by $109375$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 1050000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 1640625 + 437500 \sqrt[7]{x - 8} + 109375 \cdot 5 + 52947}{16384}$

Multiply $109375$ by $5$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 1050000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 1640625 + 437500 \sqrt[7]{x - 8} + 546875 + 52947}{16384}$

Simplify terms.

Combine the opposite terms in $16384 x - 52947 + 143360 \sqrt[7]{{(x - 8)}^{6}} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 143360 \sqrt[7]{{(x - 8)}^{6}} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 1050000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 1640625 + 437500 \sqrt[7]{x - 8} + 546875 + 52947$ .

Subtract $143360 \sqrt[7]{{(x - 8)}^{6}}$ from $143360 \sqrt[7]{{(x - 8)}^{6}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 0 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 1050000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 1640625 + 437500 \sqrt[7]{x - 8} + 546875 + 52947}{16384}$

Add $16384 x - 52947$ and $0$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 3360000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 3360000 \sqrt[7]{{(x - 8)}^{4}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 1050000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 1640625 + 437500 \sqrt[7]{x - 8} + 546875 + 52947}{16384}$

Add $- 3360000 \sqrt[7]{{(x - 8)}^{4}}$ and $3360000 \sqrt[7]{{(x - 8)}^{4}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} + 0 - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 1050000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 1640625 + 437500 \sqrt[7]{x - 8} + 546875 + 52947}{16384}$

Add $16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}}$ and $0$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1120000 \sqrt[7]{{(x - 8)}^{4}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 1120000 \sqrt[7]{{(x - 8)}^{4}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 1050000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 1640625 + 437500 \sqrt[7]{x - 8} + 546875 + 52947}{16384}$

Subtract $1120000 \sqrt[7]{{(x - 8)}^{4}}$ from $1120000 \sqrt[7]{{(x - 8)}^{4}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 0 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 1050000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 1640625 + 437500 \sqrt[7]{x - 8} + 546875 + 52947}{16384}$

Add $16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}}$ and $0$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 10500000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 10500000 \sqrt[7]{{(x - 8)}^{2}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 1050000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 1640625 + 437500 \sqrt[7]{x - 8} + 546875 + 52947}{16384}$

Subtract $10500000 \sqrt[7]{{(x - 8)}^{2}}$ from $10500000 \sqrt[7]{{(x - 8)}^{2}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 0 + 6562500 \sqrt[7]{x - 8} + 1640625 - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 1050000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 1640625 + 437500 \sqrt[7]{x - 8} + 546875 + 52947}{16384}$

Add $16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}}$ and $0$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 5250000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 5250000 \sqrt[7]{{(x - 8)}^{2}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 1050000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 1640625 + 437500 \sqrt[7]{x - 8} + 546875 + 52947}{16384}$

Add $- 5250000 \sqrt[7]{{(x - 8)}^{2}}$ and $5250000 \sqrt[7]{{(x - 8)}^{2}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} + 0 - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 1050000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 1640625 + 437500 \sqrt[7]{x - 8} + 546875 + 52947}{16384}$

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8} - 2734375 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} + 2734375 - 1050000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 1640625 + 437500 \sqrt[7]{x - 8} + 546875 + 52947}{16384}$

Add $- 2734375$ and $2734375$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8} + 0 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 1050000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 1640625 + 437500 \sqrt[7]{x - 8} + 546875 + 52947}{16384}$

Add $16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8}$ and $0$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 1050000 \sqrt[7]{{(x - 8)}^{2}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 1050000 \sqrt[7]{{(x - 8)}^{2}} - 2625000 \sqrt[7]{x - 8} - 1640625 + 437500 \sqrt[7]{x - 8} + 546875 + 52947}{16384}$

Subtract $1050000 \sqrt[7]{{(x - 8)}^{2}}$ from $1050000 \sqrt[7]{{(x - 8)}^{2}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 0 + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} - 1640625 + 437500 \sqrt[7]{x - 8} + 546875 + 52947}{16384}$

Add $16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}}$ and $0$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} + 1640625 - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} - 1640625 + 437500 \sqrt[7]{x - 8} + 546875 + 52947}{16384}$

Subtract $1640625$ from $1640625$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} + 0 - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8} + 546875 + 52947}{16384}$

Add $16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8}$ and $0$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 2625000 \sqrt[7]{x - 8} - 546875 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8} + 546875 + 52947}{16384}$

Add $- 546875$ and $546875$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 2625000 \sqrt[7]{x - 8} + 0 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8} + 52947}{16384}$

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 52947 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 2625000 \sqrt[7]{x - 8} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8} + 52947}{16384}$

Add $- 52947$ and $52947$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x + 0 + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 2625000 \sqrt[7]{x - 8} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8}}{16384}$

Add $16384 x$ and $0$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x + 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 437500 \sqrt[7]{x - 8} - 1075200 \sqrt[7]{{(x - 8)}^{5}} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 2625000 \sqrt[7]{x - 8} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8}}{16384}$

Subtract $1075200 \sqrt[7]{{(x - 8)}^{5}}$ from $537600 \sqrt[7]{{(x - 8)}^{5}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 437500 \sqrt[7]{x - 8} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 2625000 \sqrt[7]{x - 8} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8}}{16384}$

Combine the opposite terms in $16384 x - 537600 \sqrt[7]{{(x - 8)}^{5}} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 437500 \sqrt[7]{x - 8} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 2625000 \sqrt[7]{x - 8} + 537600 \sqrt[7]{{(x - 8)}^{5}} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8}$ .

Add $- 537600 \sqrt[7]{{(x - 8)}^{5}}$ and $537600 \sqrt[7]{{(x - 8)}^{5}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x + 0 + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 437500 \sqrt[7]{x - 8} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 2625000 \sqrt[7]{x - 8} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8}}{16384}$

Add $16384 x$ and $0$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 437500 \sqrt[7]{x - 8} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 2625000 \sqrt[7]{x - 8} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8}}{16384}$

Subtract $5600000 \sqrt[7]{{(x - 8)}^{3}}$ from $1400000 \sqrt[7]{{(x - 8)}^{3}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 4200000 \sqrt[7]{{(x - 8)}^{3}} + 437500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 8400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8}}{16384}$

Add $- 4200000 \sqrt[7]{{(x - 8)}^{3}}$ and $8400000 \sqrt[7]{{(x - 8)}^{3}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x + 4200000 \sqrt[7]{{(x - 8)}^{3}} + 437500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 6562500 \sqrt[7]{x - 8} - 5600000 \sqrt[7]{{(x - 8)}^{3}} - 8750000 \sqrt[7]{x - 8} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8}}{16384}$

Subtract $5600000 \sqrt[7]{{(x - 8)}^{3}}$ from $4200000 \sqrt[7]{{(x - 8)}^{3}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 1400000 \sqrt[7]{{(x - 8)}^{3}} + 437500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 6562500 \sqrt[7]{x - 8} - 8750000 \sqrt[7]{x - 8} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8}}{16384}$

Combine the opposite terms in $16384 x - 1400000 \sqrt[7]{{(x - 8)}^{3}} + 437500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 6562500 \sqrt[7]{x - 8} - 8750000 \sqrt[7]{x - 8} + 1400000 \sqrt[7]{{(x - 8)}^{3}} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8}$ .

Add $- 1400000 \sqrt[7]{{(x - 8)}^{3}}$ and $1400000 \sqrt[7]{{(x - 8)}^{3}}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x + 0 + 437500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 6562500 \sqrt[7]{x - 8} - 8750000 \sqrt[7]{x - 8} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8}}{16384}$

Add $16384 x$ and $0$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x + 437500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 6562500 \sqrt[7]{x - 8} - 8750000 \sqrt[7]{x - 8} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8}}{16384}$

Subtract $2625000 \sqrt[7]{x - 8}$ from $437500 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 2187500 \sqrt[7]{x - 8} + 6562500 \sqrt[7]{x - 8} - 8750000 \sqrt[7]{x - 8} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8}}{16384}$

Add $- 2187500 \sqrt[7]{x - 8}$ and $6562500 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x + 4375000 \sqrt[7]{x - 8} - 8750000 \sqrt[7]{x - 8} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8}}{16384}$

Subtract $8750000 \sqrt[7]{x - 8}$ from $4375000 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 4375000 \sqrt[7]{x - 8} + 6562500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8}}{16384}$

Add $- 4375000 \sqrt[7]{x - 8}$ and $6562500 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x + 2187500 \sqrt[7]{x - 8} - 2625000 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8}}{16384}$

Subtract $2625000 \sqrt[7]{x - 8}$ from $2187500 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x - 437500 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8}}{16384}$

Combine the opposite terms in $16384 x - 437500 \sqrt[7]{x - 8} + 437500 \sqrt[7]{x - 8}$ .

Add $- 437500 \sqrt[7]{x - 8}$ and $437500 \sqrt[7]{x - 8}$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x + 0}{16384}$

Add $16384 x$ and $0$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x}{16384}$

Cancel the common factor of $16384$ .

Cancel the common factor.

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = \frac{16384 x}{16384}$

Divide $x$ by $1$ .

$f^{- 1} (4 \sqrt[7]{x - 8} + 5) = x$

Evaluate $f (f^{- 1} (x))$ .

Set up the composite result function.

$f (f^{- 1} (x))$

Evaluate $f (\frac{x^{7}}{16384} - \frac{35 x^{6}}{16384} + \frac{525 x^{5}}{16384} - \frac{4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} - \frac{65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947}{16384})$ by substituting in the value of $f^{- 1}$ into $f$ .

$f (\frac{x^{7}}{16384} - \frac{35 x^{6}}{16384} + \frac{525 x^{5}}{16384} - \frac{4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} - \frac{65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947}{16384}) = 4 \sqrt[7]{(\frac{x^{7}}{16384} - \frac{35 x^{6}}{16384} + \frac{525 x^{5}}{16384} - \frac{4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} - \frac{65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947}{16384}) - 8} + 5$

Simplify each term.

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{16384}{16384}$ .

$f (\frac{x^{7}}{16384} - \frac{35 x^{6}}{16384} + \frac{525 x^{5}}{16384} - \frac{4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} - \frac{65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947}{16384}) = 4 \sqrt[7]{\frac{x^{7}}{16384} - \frac{35 x^{6}}{16384} + \frac{525 x^{5}}{16384} - \frac{4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} - \frac{65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947}{16384} - 8 \cdot \frac{16384}{16384}} + 5$

Combine $- 8$ and $\frac{16384}{16384}$ .

$f (\frac{x^{7}}{16384} - \frac{35 x^{6}}{16384} + \frac{525 x^{5}}{16384} - \frac{4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} - \frac{65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947}{16384}) = 4 \sqrt[7]{\frac{x^{7}}{16384} - \frac{35 x^{6}}{16384} + \frac{525 x^{5}}{16384} - \frac{4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} - \frac{65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947}{16384} + \frac{- 8 \cdot 16384}{16384}} + 5$

Combine the numerators over the common denominator.

$f (\frac{x^{7}}{16384} - \frac{35 x^{6}}{16384} + \frac{525 x^{5}}{16384} - \frac{4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} - \frac{65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947}{16384}) = 4 \sqrt[7]{\frac{x^{7}}{16384} - \frac{35 x^{6}}{16384} + \frac{525 x^{5}}{16384} - \frac{4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} - \frac{65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947 - 8 \cdot 16384}{16384}} + 5$

Simplify the numerator.

Multiply $- 8$ by $16384$ .

$f (\frac{x^{7}}{16384} - \frac{35 x^{6}}{16384} + \frac{525 x^{5}}{16384} - \frac{4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} - \frac{65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947}{16384}) = 4 \sqrt[7]{\frac{x^{7}}{16384} - \frac{35 x^{6}}{16384} + \frac{525 x^{5}}{16384} - \frac{4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} - \frac{65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947 - 131072}{16384}} + 5$

Subtract $131072$ from $52947$ .

$f (\frac{x^{7}}{16384} - \frac{35 x^{6}}{16384} + \frac{525 x^{5}}{16384} - \frac{4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} - \frac{65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947}{16384}) = 4 \sqrt[7]{\frac{x^{7}}{16384} - \frac{35 x^{6}}{16384} + \frac{525 x^{5}}{16384} - \frac{4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} - \frac{65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{- 78125}{16384}} + 5$

Combine the numerators over the common denominator.

$f (\frac{x^{7}}{16384} - \frac{35 x^{6}}{16384} + \frac{525 x^{5}}{16384} - \frac{4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} - \frac{65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947}{16384}) = 4 \sqrt[7]{\frac{x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 109375 x - 78125}{16384}} + 5$

Simplify the numerator.

Make each term match the terms from the binomial theorem formula.

$f (\frac{x^{7}}{16384} - \frac{35 x^{6}}{16384} + \frac{525 x^{5}}{16384} - \frac{4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} - \frac{65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947}{16384}) = 4 \sqrt[7]{\frac{x^{7} - 7 \cdot (5 x^{6}) + 21 \cdot (5^{2} x^{5}) - 35 \cdot (5^{3} x^{4}) + 35 \cdot (5^{4} x^{3}) - 21 \cdot (5^{5} x^{2}) + 7 \cdot (5^{6} x) - 1 \cdot 5^{7}}{16384}} + 5$

Factor $x^{7} - 7 \cdot 5 x^{6} + 21 \cdot 5^{2} x^{5} - 35 \cdot 5^{3} x^{4} + 35 \cdot 5^{4} x^{3} - 21 \cdot 5^{5} x^{2} + 7 \cdot 5^{6} x - 1 \cdot 5^{7}$ using the binomial theorem.

Rewrite $16384$ as $4^{7}$ .

Rewrite $\frac{{(x - 5)}^{7}}{4^{7}}$ as ${(\frac{x - 5}{4})}^{7}$ .

Pull terms out from under the radical, assuming real numbers.

Cancel the common factor of $4$ .

Cancel the common factor.

Rewrite the expression.

Combine the opposite terms in $x - 5 + 5$ .

Add $- 5$ and $5$ .

Add $x$ and $0$ .

Since $f^{- 1} (f (x)) = x$ and $f (f^{- 1} (x)) = x$ , then $f^{- 1} (x) = \frac{x^{7}}{16384} - \frac{35 x^{6}}{16384} + \frac{525 x^{5}}{16384} - \frac{4375 x^{4}}{16384} + \frac{21875 x^{3}}{16384} - \frac{65625 x^{2}}{16384} + \frac{109375 x}{16384} + \frac{52947}{16384}$ is the inverse of $f (x) = 4 \sqrt[7]{x - 8} + 5$ .

Find the Inverse f(x)=4 seventh root of x-8+5

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