Find the Inverse f(x)=( seventh root of x-8)/3

$f (x) = \frac{\sqrt[7]{x} - 8}{3}$

Write $f (x) = \frac{\sqrt[7]{x} - 8}{3}$ as an equation.

$y = \frac{\sqrt[7]{x} - 8}{3}$

Interchange the variables.

$x = \frac{\sqrt[7]{y} - 8}{3}$

Solve for $y$ .

Rewrite the equation as $\frac{\sqrt[7]{y} - 8}{3} = x$ .

$\frac{\sqrt[7]{y} - 8}{3} = x$

Multiply both sides of the equation by $3$ .

$3 \frac{\sqrt[7]{y} - 8}{3} = 3 x$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{\sqrt[7]{y} - 8}{3} = 3 x$

Rewrite the expression.

$\sqrt[7]{y} - 8 = 3 x$

Add $8$ to both sides of the equation.

$\sqrt[7]{y} = 3 x + 8$

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

${\sqrt[7]{y}}^{7} = {(3 x + 8)}^{7}$

Simplify each side of the equation.

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

${(y^{\frac{1}{7}})}^{7} = {(3 x + 8)}^{7}$

Simplify the left side.

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

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

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

$y^{\frac{1}{7} \cdot 7} = {(3 x + 8)}^{7}$

Cancel the common factor of $7$ .

Cancel the common factor.

$y^{\frac{1}{7} \cdot 7} = {(3 x + 8)}^{7}$

Rewrite the expression.

$y^{1} = {(3 x + 8)}^{7}$

Simplify.

$y = {(3 x + 8)}^{7}$

Simplify the right side.

Simplify ${(3 x + 8)}^{7}$ .

Use the Binomial Theorem.

$y = {(3 x)}^{7} + 7 {(3 x)}^{6} \cdot 8 + 21 {(3 x)}^{5} \cdot 8^{2} + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Simplify each term.

Apply the product rule to $3 x$ .

$y = 3^{7} x^{7} + 7 {(3 x)}^{6} \cdot 8 + 21 {(3 x)}^{5} \cdot 8^{2} + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Raise $3$ to the power of $7$ .

$y = 2187 x^{7} + 7 {(3 x)}^{6} \cdot 8 + 21 {(3 x)}^{5} \cdot 8^{2} + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Apply the product rule to $3 x$ .

$y = 2187 x^{7} + 7 (3^{6} x^{6}) \cdot 8 + 21 {(3 x)}^{5} \cdot 8^{2} + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Raise $3$ to the power of $6$ .

$y = 2187 x^{7} + 7 (729 x^{6}) \cdot 8 + 21 {(3 x)}^{5} \cdot 8^{2} + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Multiply $729$ by $7$ .

$y = 2187 x^{7} + 5103 x^{6} \cdot 8 + 21 {(3 x)}^{5} \cdot 8^{2} + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Multiply $8$ by $5103$ .

$y = 2187 x^{7} + 40824 x^{6} + 21 {(3 x)}^{5} \cdot 8^{2} + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Apply the product rule to $3 x$ .

$y = 2187 x^{7} + 40824 x^{6} + 21 (3^{5} x^{5}) \cdot 8^{2} + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

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

$y = 2187 x^{7} + 40824 x^{6} + 21 (243 x^{5}) \cdot 8^{2} + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Multiply $243$ by $21$ .

$y = 2187 x^{7} + 40824 x^{6} + 5103 x^{5} \cdot 8^{2} + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Raise $8$ to the power of $2$ .

$y = 2187 x^{7} + 40824 x^{6} + 5103 x^{5} \cdot 64 + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Multiply $64$ by $5103$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Apply the product rule to $3 x$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 35 (3^{4} x^{4}) \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

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

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 35 (81 x^{4}) \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Multiply $81$ by $35$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 2835 x^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Raise $8$ to the power of $3$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 2835 x^{4} \cdot 512 + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Multiply $512$ by $2835$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Apply the product rule to $3 x$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 35 (3^{3} x^{3}) \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

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

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 35 (27 x^{3}) \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Multiply $27$ by $35$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 945 x^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Raise $8$ to the power of $4$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 945 x^{3} \cdot 4096 + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Multiply $4096$ by $945$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Apply the product rule to $3 x$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 21 (3^{2} x^{2}) \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Raise $3$ to the power of $2$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 21 (9 x^{2}) \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Multiply $9$ by $21$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 189 x^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Raise $8$ to the power of $5$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 189 x^{2} \cdot 32768 + 7 (3 x) \cdot 8^{6} + 8^{7}$

Multiply $32768$ by $189$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Multiply $3$ by $7$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 21 x \cdot 8^{6} + 8^{7}$

Raise $8$ to the power of $6$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 21 x \cdot 262144 + 8^{7}$

Multiply $262144$ by $21$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 5505024 x + 8^{7}$

Raise $8$ to the power of $7$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 5505024 x + 2097152$

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

$f^{- 1} (x) = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 5505024 x + 2097152$

Verify if $f^{- 1} (x) = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 5505024 x + 2097152$ is the inverse of $f (x) = \frac{\sqrt[7]{x} - 8}{3}$ .

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 $f^{- 1} (\frac{\sqrt[7]{x} - 8}{3})$ by substituting in the value of $f$ into $f^{- 1}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = 2187 {(\frac{\sqrt[7]{x} - 8}{3})}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Simplify each term.

Apply the product rule to $\frac{\sqrt[7]{x} - 8}{3}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = 2187 (\frac{{(\sqrt[7]{x} - 8)}^{7}}{3^{7}}) + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $3$ to the power of $7$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = 2187 (\frac{{(\sqrt[7]{x} - 8)}^{7}}{2187}) + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Cancel the common factor of $2187$ .

Cancel the common factor.

Rewrite the expression.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = {(\sqrt[7]{x} - 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Use the Binomial Theorem.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = {\sqrt[7]{x}}^{7} + 7 {\sqrt[7]{x}}^{6} \cdot - 8 + 21 {\sqrt[7]{x}}^{5} {(- 8)}^{2} + 35 {\sqrt[7]{x}}^{4} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Simplify each term.

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

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = {(x^{\frac{1}{7}})}^{7} + 7 {\sqrt[7]{x}}^{6} \cdot - 8 + 21 {\sqrt[7]{x}}^{5} {(- 8)}^{2} + 35 {\sqrt[7]{x}}^{4} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x^{\frac{1}{7} \cdot 7} + 7 {\sqrt[7]{x}}^{6} \cdot - 8 + 21 {\sqrt[7]{x}}^{5} {(- 8)}^{2} + 35 {\sqrt[7]{x}}^{4} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x^{\frac{7}{7}} + 7 {\sqrt[7]{x}}^{6} \cdot - 8 + 21 {\sqrt[7]{x}}^{5} {(- 8)}^{2} + 35 {\sqrt[7]{x}}^{4} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Cancel the common factor of $7$ .

Cancel the common factor.

Rewrite the expression.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 7 {\sqrt[7]{x}}^{6} \cdot - 8 + 21 {\sqrt[7]{x}}^{5} {(- 8)}^{2} + 35 {\sqrt[7]{x}}^{4} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Simplify.

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 7 \sqrt[7]{x^{6}} \cdot - 8 + 21 {\sqrt[7]{x}}^{5} {(- 8)}^{2} + 35 {\sqrt[7]{x}}^{4} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $- 8$ by $7$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 21 {\sqrt[7]{x}}^{5} {(- 8)}^{2} + 35 {\sqrt[7]{x}}^{4} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 21 \sqrt[7]{x^{5}} {(- 8)}^{2} + 35 {\sqrt[7]{x}}^{4} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $- 8$ to the power of $2$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 21 \sqrt[7]{x^{5}} \cdot 64 + 35 {\sqrt[7]{x}}^{4} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $64$ by $21$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} + 35 {\sqrt[7]{x}}^{4} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} + 35 \sqrt[7]{x^{4}} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $- 8$ to the power of $3$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} + 35 \sqrt[7]{x^{4}} \cdot - 512 + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $- 512$ by $35$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 35 \sqrt[7]{x^{3}} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $- 8$ to the power of $4$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 35 \sqrt[7]{x^{3}} \cdot 4096 + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $4096$ by $35$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} + 21 \sqrt[7]{x^{2}} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $- 8$ to the power of $5$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} + 21 \sqrt[7]{x^{2}} \cdot - 32768 + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $- 32768$ by $21$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $- 8$ to the power of $6$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 7 \sqrt[7]{x} \cdot 262144 + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $262144$ by $7$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $- 8$ to the power of $7$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Apply the product rule to $\frac{\sqrt[7]{x} - 8}{3}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 40824 (\frac{{(\sqrt[7]{x} - 8)}^{6}}{3^{6}}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $3$ to the power of $6$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 40824 (\frac{{(\sqrt[7]{x} - 8)}^{6}}{729}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Cancel the common factor of $729$ .

Factor $729$ out of $40824$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 729 (56) (\frac{{(\sqrt[7]{x} - 8)}^{6}}{729}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Cancel the common factor.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 729 \cdot (56 (\frac{{(\sqrt[7]{x} - 8)}^{6}}{729})) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Rewrite the expression.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 {(\sqrt[7]{x} - 8)}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Use the Binomial Theorem.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 ({\sqrt[7]{x}}^{6} + 6 {\sqrt[7]{x}}^{5} \cdot - 8 + 15 {\sqrt[7]{x}}^{4} {(- 8)}^{2} + 20 {\sqrt[7]{x}}^{3} {(- 8)}^{3} + 15 {\sqrt[7]{x}}^{2} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Simplify each term.

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} + 6 {\sqrt[7]{x}}^{5} \cdot - 8 + 15 {\sqrt[7]{x}}^{4} {(- 8)}^{2} + 20 {\sqrt[7]{x}}^{3} {(- 8)}^{3} + 15 {\sqrt[7]{x}}^{2} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} + 6 \sqrt[7]{x^{5}} \cdot - 8 + 15 {\sqrt[7]{x}}^{4} {(- 8)}^{2} + 20 {\sqrt[7]{x}}^{3} {(- 8)}^{3} + 15 {\sqrt[7]{x}}^{2} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $- 8$ by $6$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 15 {\sqrt[7]{x}}^{4} {(- 8)}^{2} + 20 {\sqrt[7]{x}}^{3} {(- 8)}^{3} + 15 {\sqrt[7]{x}}^{2} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 15 \sqrt[7]{x^{4}} {(- 8)}^{2} + 20 {\sqrt[7]{x}}^{3} {(- 8)}^{3} + 15 {\sqrt[7]{x}}^{2} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $- 8$ to the power of $2$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 15 \sqrt[7]{x^{4}} \cdot 64 + 20 {\sqrt[7]{x}}^{3} {(- 8)}^{3} + 15 {\sqrt[7]{x}}^{2} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $64$ by $15$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 960 \sqrt[7]{x^{4}} + 20 {\sqrt[7]{x}}^{3} {(- 8)}^{3} + 15 {\sqrt[7]{x}}^{2} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 960 \sqrt[7]{x^{4}} + 20 \sqrt[7]{x^{3}} {(- 8)}^{3} + 15 {\sqrt[7]{x}}^{2} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $- 8$ to the power of $3$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 960 \sqrt[7]{x^{4}} + 20 \sqrt[7]{x^{3}} \cdot - 512 + 15 {\sqrt[7]{x}}^{2} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $- 512$ by $20$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 960 \sqrt[7]{x^{4}} - 10240 \sqrt[7]{x^{3}} + 15 {\sqrt[7]{x}}^{2} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 960 \sqrt[7]{x^{4}} - 10240 \sqrt[7]{x^{3}} + 15 \sqrt[7]{x^{2}} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $- 8$ to the power of $4$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 960 \sqrt[7]{x^{4}} - 10240 \sqrt[7]{x^{3}} + 15 \sqrt[7]{x^{2}} \cdot 4096 + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $4096$ by $15$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 960 \sqrt[7]{x^{4}} - 10240 \sqrt[7]{x^{3}} + 61440 \sqrt[7]{x^{2}} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $- 8$ to the power of $5$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 960 \sqrt[7]{x^{4}} - 10240 \sqrt[7]{x^{3}} + 61440 \sqrt[7]{x^{2}} + 6 \sqrt[7]{x} \cdot - 32768 + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $- 32768$ by $6$ .

Raise $- 8$ to the power of $6$ .

Apply the distributive property.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} + 56 (- 48 \sqrt[7]{x^{5}}) + 56 (960 \sqrt[7]{x^{4}}) + 56 (- 10240 \sqrt[7]{x^{3}}) + 56 (61440 \sqrt[7]{x^{2}}) + 56 (- 196608 \sqrt[7]{x}) + 56 \cdot 262144 + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Simplify.

Multiply $- 48$ by $56$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 56 (960 \sqrt[7]{x^{4}}) + 56 (- 10240 \sqrt[7]{x^{3}}) + 56 (61440 \sqrt[7]{x^{2}}) + 56 (- 196608 \sqrt[7]{x}) + 56 \cdot 262144 + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $960$ by $56$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} + 56 (- 10240 \sqrt[7]{x^{3}}) + 56 (61440 \sqrt[7]{x^{2}}) + 56 (- 196608 \sqrt[7]{x}) + 56 \cdot 262144 + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $- 10240$ by $56$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 56 (61440 \sqrt[7]{x^{2}}) + 56 (- 196608 \sqrt[7]{x}) + 56 \cdot 262144 + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $61440$ by $56$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} + 56 (- 196608 \sqrt[7]{x}) + 56 \cdot 262144 + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $- 196608$ by $56$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 56 \cdot 262144 + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $56$ by $262144$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Apply the product rule to $\frac{\sqrt[7]{x} - 8}{3}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 326592 (\frac{{(\sqrt[7]{x} - 8)}^{5}}{3^{5}}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 326592 (\frac{{(\sqrt[7]{x} - 8)}^{5}}{243}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Cancel the common factor of $243$ .

Factor $243$ out of $326592$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 243 (1344) (\frac{{(\sqrt[7]{x} - 8)}^{5}}{243}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Cancel the common factor.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 243 \cdot (1344 (\frac{{(\sqrt[7]{x} - 8)}^{5}}{243})) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Rewrite the expression.

Use the Binomial Theorem.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 ({\sqrt[7]{x}}^{5} + 5 {\sqrt[7]{x}}^{4} \cdot - 8 + 10 {\sqrt[7]{x}}^{3} {(- 8)}^{2} + 10 {\sqrt[7]{x}}^{2} {(- 8)}^{3} + 5 \sqrt[7]{x} {(- 8)}^{4} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Simplify each term.

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} + 5 {\sqrt[7]{x}}^{4} \cdot - 8 + 10 {\sqrt[7]{x}}^{3} {(- 8)}^{2} + 10 {\sqrt[7]{x}}^{2} {(- 8)}^{3} + 5 \sqrt[7]{x} {(- 8)}^{4} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} + 5 \sqrt[7]{x^{4}} \cdot - 8 + 10 {\sqrt[7]{x}}^{3} {(- 8)}^{2} + 10 {\sqrt[7]{x}}^{2} {(- 8)}^{3} + 5 \sqrt[7]{x} {(- 8)}^{4} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $- 8$ by $5$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} - 40 \sqrt[7]{x^{4}} + 10 {\sqrt[7]{x}}^{3} {(- 8)}^{2} + 10 {\sqrt[7]{x}}^{2} {(- 8)}^{3} + 5 \sqrt[7]{x} {(- 8)}^{4} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} - 40 \sqrt[7]{x^{4}} + 10 \sqrt[7]{x^{3}} {(- 8)}^{2} + 10 {\sqrt[7]{x}}^{2} {(- 8)}^{3} + 5 \sqrt[7]{x} {(- 8)}^{4} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $- 8$ to the power of $2$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} - 40 \sqrt[7]{x^{4}} + 10 \sqrt[7]{x^{3}} \cdot 64 + 10 {\sqrt[7]{x}}^{2} {(- 8)}^{3} + 5 \sqrt[7]{x} {(- 8)}^{4} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $64$ by $10$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} - 40 \sqrt[7]{x^{4}} + 640 \sqrt[7]{x^{3}} + 10 {\sqrt[7]{x}}^{2} {(- 8)}^{3} + 5 \sqrt[7]{x} {(- 8)}^{4} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} - 40 \sqrt[7]{x^{4}} + 640 \sqrt[7]{x^{3}} + 10 \sqrt[7]{x^{2}} {(- 8)}^{3} + 5 \sqrt[7]{x} {(- 8)}^{4} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $- 8$ to the power of $3$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} - 40 \sqrt[7]{x^{4}} + 640 \sqrt[7]{x^{3}} + 10 \sqrt[7]{x^{2}} \cdot - 512 + 5 \sqrt[7]{x} {(- 8)}^{4} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $- 512$ by $10$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} - 40 \sqrt[7]{x^{4}} + 640 \sqrt[7]{x^{3}} - 5120 \sqrt[7]{x^{2}} + 5 \sqrt[7]{x} {(- 8)}^{4} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $- 8$ to the power of $4$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} - 40 \sqrt[7]{x^{4}} + 640 \sqrt[7]{x^{3}} - 5120 \sqrt[7]{x^{2}} + 5 \sqrt[7]{x} \cdot 4096 + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $4096$ by $5$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} - 40 \sqrt[7]{x^{4}} + 640 \sqrt[7]{x^{3}} - 5120 \sqrt[7]{x^{2}} + 20480 \sqrt[7]{x} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $- 8$ to the power of $5$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} - 40 \sqrt[7]{x^{4}} + 640 \sqrt[7]{x^{3}} - 5120 \sqrt[7]{x^{2}} + 20480 \sqrt[7]{x} - 32768) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Apply the distributive property.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 1344 (- 40 \sqrt[7]{x^{4}}) + 1344 (640 \sqrt[7]{x^{3}}) + 1344 (- 5120 \sqrt[7]{x^{2}}) + 1344 (20480 \sqrt[7]{x}) + 1344 \cdot - 32768 + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Simplify.

Multiply $- 40$ by $1344$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 1344 (640 \sqrt[7]{x^{3}}) + 1344 (- 5120 \sqrt[7]{x^{2}}) + 1344 (20480 \sqrt[7]{x}) + 1344 \cdot - 32768 + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $640$ by $1344$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} + 1344 (- 5120 \sqrt[7]{x^{2}}) + 1344 (20480 \sqrt[7]{x}) + 1344 \cdot - 32768 + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $- 5120$ by $1344$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 1344 (20480 \sqrt[7]{x}) + 1344 \cdot - 32768 + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $20480$ by $1344$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} + 1344 \cdot - 32768 + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $1344$ by $- 32768$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Apply the product rule to $\frac{\sqrt[7]{x} - 8}{3}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 1451520 (\frac{{(\sqrt[7]{x} - 8)}^{4}}{3^{4}}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 1451520 (\frac{{(\sqrt[7]{x} - 8)}^{4}}{81}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Cancel the common factor of $81$ .

Factor $81$ out of $1451520$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 81 (17920) (\frac{{(\sqrt[7]{x} - 8)}^{4}}{81}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Cancel the common factor.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 81 \cdot (17920 (\frac{{(\sqrt[7]{x} - 8)}^{4}}{81})) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Rewrite the expression.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 {(\sqrt[7]{x} - 8)}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Use the Binomial Theorem.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 ({\sqrt[7]{x}}^{4} + 4 {\sqrt[7]{x}}^{3} \cdot - 8 + 6 {\sqrt[7]{x}}^{2} {(- 8)}^{2} + 4 \sqrt[7]{x} {(- 8)}^{3} + {(- 8)}^{4}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Simplify each term.

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 (\sqrt[7]{x^{4}} + 4 {\sqrt[7]{x}}^{3} \cdot - 8 + 6 {\sqrt[7]{x}}^{2} {(- 8)}^{2} + 4 \sqrt[7]{x} {(- 8)}^{3} + {(- 8)}^{4}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 (\sqrt[7]{x^{4}} + 4 \sqrt[7]{x^{3}} \cdot - 8 + 6 {\sqrt[7]{x}}^{2} {(- 8)}^{2} + 4 \sqrt[7]{x} {(- 8)}^{3} + {(- 8)}^{4}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $- 8$ by $4$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 (\sqrt[7]{x^{4}} - 32 \sqrt[7]{x^{3}} + 6 {\sqrt[7]{x}}^{2} {(- 8)}^{2} + 4 \sqrt[7]{x} {(- 8)}^{3} + {(- 8)}^{4}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 (\sqrt[7]{x^{4}} - 32 \sqrt[7]{x^{3}} + 6 \sqrt[7]{x^{2}} {(- 8)}^{2} + 4 \sqrt[7]{x} {(- 8)}^{3} + {(- 8)}^{4}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $- 8$ to the power of $2$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 (\sqrt[7]{x^{4}} - 32 \sqrt[7]{x^{3}} + 6 \sqrt[7]{x^{2}} \cdot 64 + 4 \sqrt[7]{x} {(- 8)}^{3} + {(- 8)}^{4}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $64$ by $6$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 (\sqrt[7]{x^{4}} - 32 \sqrt[7]{x^{3}} + 384 \sqrt[7]{x^{2}} + 4 \sqrt[7]{x} {(- 8)}^{3} + {(- 8)}^{4}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $- 8$ to the power of $3$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 (\sqrt[7]{x^{4}} - 32 \sqrt[7]{x^{3}} + 384 \sqrt[7]{x^{2}} + 4 \sqrt[7]{x} \cdot - 512 + {(- 8)}^{4}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $- 512$ by $4$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 (\sqrt[7]{x^{4}} - 32 \sqrt[7]{x^{3}} + 384 \sqrt[7]{x^{2}} - 2048 \sqrt[7]{x} + {(- 8)}^{4}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $- 8$ to the power of $4$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 (\sqrt[7]{x^{4}} - 32 \sqrt[7]{x^{3}} + 384 \sqrt[7]{x^{2}} - 2048 \sqrt[7]{x} + 4096) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Apply the distributive property.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} + 17920 (- 32 \sqrt[7]{x^{3}}) + 17920 (384 \sqrt[7]{x^{2}}) + 17920 (- 2048 \sqrt[7]{x}) + 17920 \cdot 4096 + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Simplify.

Multiply $- 32$ by $17920$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 17920 (384 \sqrt[7]{x^{2}}) + 17920 (- 2048 \sqrt[7]{x}) + 17920 \cdot 4096 + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $384$ by $17920$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} + 17920 (- 2048 \sqrt[7]{x}) + 17920 \cdot 4096 + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $- 2048$ by $17920$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 17920 \cdot 4096 + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $17920$ by $4096$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Apply the product rule to $\frac{\sqrt[7]{x} - 8}{3}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 3870720 (\frac{{(\sqrt[7]{x} - 8)}^{3}}{3^{3}}) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 3870720 (\frac{{(\sqrt[7]{x} - 8)}^{3}}{27}) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Cancel the common factor of $27$ .

Factor $27$ out of $3870720$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 27 (143360) (\frac{{(\sqrt[7]{x} - 8)}^{3}}{27}) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Cancel the common factor.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 27 \cdot (143360 (\frac{{(\sqrt[7]{x} - 8)}^{3}}{27})) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Rewrite the expression.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 {(\sqrt[7]{x} - 8)}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Use the Binomial Theorem.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 ({\sqrt[7]{x}}^{3} + 3 {\sqrt[7]{x}}^{2} \cdot - 8 + 3 \sqrt[7]{x} {(- 8)}^{2} + {(- 8)}^{3}) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Simplify each term.

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 (\sqrt[7]{x^{3}} + 3 {\sqrt[7]{x}}^{2} \cdot - 8 + 3 \sqrt[7]{x} {(- 8)}^{2} + {(- 8)}^{3}) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 (\sqrt[7]{x^{3}} + 3 \sqrt[7]{x^{2}} \cdot - 8 + 3 \sqrt[7]{x} {(- 8)}^{2} + {(- 8)}^{3}) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $- 8$ by $3$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 (\sqrt[7]{x^{3}} - 24 \sqrt[7]{x^{2}} + 3 \sqrt[7]{x} {(- 8)}^{2} + {(- 8)}^{3}) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $- 8$ to the power of $2$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 (\sqrt[7]{x^{3}} - 24 \sqrt[7]{x^{2}} + 3 \sqrt[7]{x} \cdot 64 + {(- 8)}^{3}) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $64$ by $3$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 (\sqrt[7]{x^{3}} - 24 \sqrt[7]{x^{2}} + 192 \sqrt[7]{x} + {(- 8)}^{3}) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $- 8$ to the power of $3$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 (\sqrt[7]{x^{3}} - 24 \sqrt[7]{x^{2}} + 192 \sqrt[7]{x} - 512) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Apply the distributive property.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} + 143360 (- 24 \sqrt[7]{x^{2}}) + 143360 (192 \sqrt[7]{x}) + 143360 \cdot - 512 + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Simplify.

Multiply $- 24$ by $143360$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 143360 (192 \sqrt[7]{x}) + 143360 \cdot - 512 + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $192$ by $143360$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} + 143360 \cdot - 512 + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $143360$ by $- 512$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Apply the product rule to $\frac{\sqrt[7]{x} - 8}{3}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 6193152 (\frac{{(\sqrt[7]{x} - 8)}^{2}}{3^{2}}) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Raise $3$ to the power of $2$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 6193152 (\frac{{(\sqrt[7]{x} - 8)}^{2}}{9}) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Cancel the common factor of $9$ .

Factor $9$ out of $6193152$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 9 (688128) (\frac{{(\sqrt[7]{x} - 8)}^{2}}{9}) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Cancel the common factor.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 9 \cdot (688128 (\frac{{(\sqrt[7]{x} - 8)}^{2}}{9})) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Rewrite the expression.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 {(\sqrt[7]{x} - 8)}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 ((\sqrt[7]{x} - 8) (\sqrt[7]{x} - 8)) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

Apply the distributive property.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 (\sqrt[7]{x} (\sqrt[7]{x} - 8) - 8 (\sqrt[7]{x} - 8)) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Apply the distributive property.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 (\sqrt[7]{x} \sqrt[7]{x} + \sqrt[7]{x} \cdot - 8 - 8 (\sqrt[7]{x} - 8)) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Apply the distributive property.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 (\sqrt[7]{x} \sqrt[7]{x} + \sqrt[7]{x} \cdot - 8 - 8 \sqrt[7]{x} - 8 \cdot - 8) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Simplify and combine like terms.

Simplify each term.

Multiply $\sqrt[7]{x} \sqrt[7]{x}$ .

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 (\sqrt[7]{x} \sqrt[7]{x} + \sqrt[7]{x} \cdot - 8 - 8 \sqrt[7]{x} - 8 \cdot - 8) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 (\sqrt[7]{x} \sqrt[7]{x} + \sqrt[7]{x} \cdot - 8 - 8 \sqrt[7]{x} - 8 \cdot - 8) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 ({\sqrt[7]{x}}^{1 + 1} + \sqrt[7]{x} \cdot - 8 - 8 \sqrt[7]{x} - 8 \cdot - 8) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Add $1$ and $1$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 ({\sqrt[7]{x}}^{2} + \sqrt[7]{x} \cdot - 8 - 8 \sqrt[7]{x} - 8 \cdot - 8) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 (\sqrt[7]{x^{2}} + \sqrt[7]{x} \cdot - 8 - 8 \sqrt[7]{x} - 8 \cdot - 8) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Move $- 8$ to the left of $\sqrt[7]{x}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 (\sqrt[7]{x^{2}} - 8 \cdot \sqrt[7]{x} - 8 \sqrt[7]{x} - 8 \cdot - 8) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $- 8$ by $- 8$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 (\sqrt[7]{x^{2}} - 8 \sqrt[7]{x} - 8 \sqrt[7]{x} + 64) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 (\sqrt[7]{x^{2}} - 16 \sqrt[7]{x} + 64) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Apply the distributive property.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} + 688128 (- 16 \sqrt[7]{x}) + 688128 \cdot 64 + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Simplify.

Multiply $- 16$ by $688128$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 688128 \cdot 64 + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Multiply $688128$ by $64$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Cancel the common factor of $3$ .

Factor $3$ out of $5505024$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 3 (1835008) (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Cancel the common factor.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 3 \cdot (1835008 (\frac{\sqrt[7]{x} - 8}{3})) + 2097152$

Rewrite the expression.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 (\sqrt[7]{x} - 8) + 2097152$

Apply the distributive property.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} + 1835008 \cdot - 8 + 2097152$

Multiply $1835008$ by $- 8$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Simplify by adding terms.

Combine the opposite terms in $x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$ .

Add $- 56 \sqrt[7]{x^{6}}$ and $56 \sqrt[7]{x^{6}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 0 + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Add $x$ and $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Subtract $53760 \sqrt[7]{x^{4}}$ from $53760 \sqrt[7]{x^{4}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} + 0 - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Add $x + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}}$ and $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Add $- 17920 \sqrt[7]{x^{4}}$ and $17920 \sqrt[7]{x^{4}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 0 + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Add $x + 1344 \sqrt[7]{x^{5}}$ and $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Add $- 6881280 \sqrt[7]{x^{2}}$ and $6881280 \sqrt[7]{x^{2}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 0 + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Add $x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}}$ and $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Subtract $3440640 \sqrt[7]{x^{2}}$ from $3440640 \sqrt[7]{x^{2}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} + 0 - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Add $x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}}$ and $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Subtract $73400320$ from $73400320$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 0 + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Add $x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x}$ and $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Add $- 688128 \sqrt[7]{x^{2}}$ and $688128 \sqrt[7]{x^{2}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 0 + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Add $x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}}$ and $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Add $- 44040192$ and $44040192$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} + 0 - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Add $x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x}$ and $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Subtract $14680064$ from $14680064$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 0 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x} + 2097152$

Add $x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x}$ and $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x} + 2097152$

Add $- 2097152$ and $2097152$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} + 0 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Add $x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x}$ and $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Subtract $2688 \sqrt[7]{x^{5}}$ from $1344 \sqrt[7]{x^{5}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Combine the opposite terms in $x - 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$ .

Add $- 1344 \sqrt[7]{x^{5}}$ and $1344 \sqrt[7]{x^{5}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 0 + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Add $x$ and $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Subtract $573440 \sqrt[7]{x^{3}}$ from $143360 \sqrt[7]{x^{3}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 430080 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Add $- 430080 \sqrt[7]{x^{3}}$ and $860160 \sqrt[7]{x^{3}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 430080 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Subtract $573440 \sqrt[7]{x^{3}}$ from $430080 \sqrt[7]{x^{3}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Combine the opposite terms in $x - 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$ .

Add $- 143360 \sqrt[7]{x^{3}}$ and $143360 \sqrt[7]{x^{3}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 0 + 1835008 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 36700160 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Add $x$ and $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1835008 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 36700160 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Subtract $11010048 \sqrt[7]{x}$ from $1835008 \sqrt[7]{x}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 9175040 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 36700160 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Add $- 9175040 \sqrt[7]{x}$ and $27525120 \sqrt[7]{x}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 18350080 \sqrt[7]{x} - 36700160 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Subtract $36700160 \sqrt[7]{x}$ from $18350080 \sqrt[7]{x}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 18350080 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Add $- 18350080 \sqrt[7]{x}$ and $27525120 \sqrt[7]{x}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 9175040 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Subtract $11010048 \sqrt[7]{x}$ from $9175040 \sqrt[7]{x}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 1835008 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Combine the opposite terms in $x - 1835008 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$ .

Add $- 1835008 \sqrt[7]{x}$ and $1835008 \sqrt[7]{x}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 0$

Add $x$ and $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x$

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

Set up the composite result function.

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

Evaluate $f (2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 5505024 x + 2097152)$ by substituting in the value of $f^{- 1}$ into $f$ .

$f (2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 5505024 x + 2097152) = \frac{\sqrt[7]{2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 5505024 x + 2097152} - 8}{3}$

Since $f^{- 1} (f (x)) = x$ and $f (f^{- 1} (x)) = x$ , then $f^{- 1} (x) = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 5505024 x + 2097152$ is the inverse of $f (x) = \frac{\sqrt[7]{x} - 8}{3}$ .

$f^{- 1} (x) = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 5505024 x + 2097152$

Find the Inverse f(x)=( seventh root of x-8)/3

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