Find the Inverse f(x)=((x-7)^(1/5))/7+9

$f (x) = \frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9$

Write $f (x) = \frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9$ as an equation.

$y = \frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9$

Interchange the variables.

$x = \frac{{(y - 7)}^{\frac{1}{5}}}{7} + 9$

Solve for $y$ .

Rewrite the equation as $\frac{{(y - 7)}^{\frac{1}{5}}}{7} + 9 = x$ .

$\frac{{(y - 7)}^{\frac{1}{5}}}{7} + 9 = x$

Simplify $\frac{{(y - 7)}^{\frac{1}{5}}}{7} + 9$ .

To write $9$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{{(y - 7)}^{\frac{1}{5}}}{7} + 9 \cdot \frac{7}{7} = x$

Combine $9$ and $\frac{7}{7}$ .

$\frac{{(y - 7)}^{\frac{1}{5}}}{7} + \frac{9 \cdot 7}{7} = x$

Combine the numerators over the common denominator.

$\frac{{(y - 7)}^{\frac{1}{5}} + 9 \cdot 7}{7} = x$

Multiply $9$ by $7$ .

$\frac{{(y - 7)}^{\frac{1}{5}} + 63}{7} = x$

Multiply both sides of the equation by $7$ .

$7 \frac{{(y - 7)}^{\frac{1}{5}} + 63}{7} = 7 x$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$7 \frac{{(y - 7)}^{\frac{1}{5}} + 63}{7} = 7 x$

Rewrite the expression.

${(y - 7)}^{\frac{1}{5}} + 63 = 7 x$

Subtract $63$ from both sides of the equation.

${(y - 7)}^{\frac{1}{5}} = 7 x - 63$

Raise each side of the equation to the power of $5$ to eliminate the fractional exponent on the left side.

${({(y - 7)}^{\frac{1}{5}})}^{5} = {(7 x - 63)}^{5}$

Simplify the exponent.

Simplify the left side.

Simplify ${({(y - 7)}^{\frac{1}{5}})}^{5}$ .

Multiply the exponents in ${({(y - 7)}^{\frac{1}{5}})}^{5}$ .

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

${(y - 7)}^{\frac{1}{5} \cdot 5} = {(7 x - 63)}^{5}$

Cancel the common factor of $5$ .

Cancel the common factor.

${(y - 7)}^{\frac{1}{5} \cdot 5} = {(7 x - 63)}^{5}$

Rewrite the expression.

${(y - 7)}^{1} = {(7 x - 63)}^{5}$

Simplify.

$y - 7 = {(7 x - 63)}^{5}$

Simplify the right side.

Simplify ${(7 x - 63)}^{5}$ .

Use the Binomial Theorem.

$y - 7 = {(7 x)}^{5} + 5 {(7 x)}^{4} \cdot - 63 + 10 {(7 x)}^{3} {(- 63)}^{2} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Simplify each term.

Apply the product rule to $7 x$ .

$y - 7 = 7^{5} x^{5} + 5 {(7 x)}^{4} \cdot - 63 + 10 {(7 x)}^{3} {(- 63)}^{2} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

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

$y - 7 = 16807 x^{5} + 5 {(7 x)}^{4} \cdot - 63 + 10 {(7 x)}^{3} {(- 63)}^{2} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Apply the product rule to $7 x$ .

$y - 7 = 16807 x^{5} + 5 (7^{4} x^{4}) \cdot - 63 + 10 {(7 x)}^{3} {(- 63)}^{2} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

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

$y - 7 = 16807 x^{5} + 5 (2401 x^{4}) \cdot - 63 + 10 {(7 x)}^{3} {(- 63)}^{2} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Multiply $2401$ by $5$ .

$y - 7 = 16807 x^{5} + 12005 x^{4} \cdot - 63 + 10 {(7 x)}^{3} {(- 63)}^{2} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Multiply $- 63$ by $12005$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 10 {(7 x)}^{3} {(- 63)}^{2} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Apply the product rule to $7 x$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 10 (7^{3} x^{3}) {(- 63)}^{2} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

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

$y - 7 = 16807 x^{5} - 756315 x^{4} + 10 (343 x^{3}) {(- 63)}^{2} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Multiply $343$ by $10$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 3430 x^{3} {(- 63)}^{2} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Raise $- 63$ to the power of $2$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 3430 x^{3} \cdot 3969 + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Multiply $3969$ by $3430$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Apply the product rule to $7 x$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} + 10 (7^{2} x^{2}) {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Raise $7$ to the power of $2$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} + 10 (49 x^{2}) {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Multiply $49$ by $10$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} + 490 x^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Raise $- 63$ to the power of $3$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} + 490 x^{2} \cdot - 250047 + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Multiply $- 250047$ by $490$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Multiply $7$ by $5$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 35 x {(- 63)}^{4} + {(- 63)}^{5}$

Raise $- 63$ to the power of $4$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 35 x \cdot 15752961 + {(- 63)}^{5}$

Multiply $15752961$ by $35$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x + {(- 63)}^{5}$

Raise $- 63$ to the power of $5$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436543$

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

Add $7$ to both sides of the equation.

$y = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436543 + 7$

Add $- 992436543$ and $7$ .

$y = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436536$

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

$f^{- 1} (x) = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436536$

Verify if $f^{- 1} (x) = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436536$ is the inverse of $f (x) = \frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9$ .

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 $f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)$ by substituting in the value of $f$ into $f^{- 1}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = 16807 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Simplify each term.

To write $9$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = 16807 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9 \cdot \frac{7}{7})}^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Combine $9$ and $\frac{7}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = 16807 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + \frac{9 \cdot 7}{7})}^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Combine the numerators over the common denominator.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = 16807 {(\frac{{(x - 7)}^{\frac{1}{5}} + 9 \cdot 7}{7})}^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply $9$ by $7$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = 16807 {(\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7})}^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Apply the product rule to $\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = 16807 (\frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{5}}{7^{5}}) - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

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

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = 16807 (\frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{5}}{16807}) - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Cancel the common factor of $16807$ .

Cancel the common factor.

Rewrite the expression.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = {({(x - 7)}^{\frac{1}{5}} + 63)}^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Use the Binomial Theorem.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = {({(x - 7)}^{\frac{1}{5}})}^{5} + 5 {({(x - 7)}^{\frac{1}{5}})}^{4} \cdot 63 + 10 {({(x - 7)}^{\frac{1}{5}})}^{3} \cdot 63^{2} + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Simplify each term.

Multiply the exponents in ${({(x - 7)}^{\frac{1}{5}})}^{5}$ .

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

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = {(x - 7)}^{\frac{1}{5} \cdot 5} + 5 {({(x - 7)}^{\frac{1}{5}})}^{4} \cdot 63 + 10 {({(x - 7)}^{\frac{1}{5}})}^{3} \cdot 63^{2} + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Cancel the common factor of $5$ .

Cancel the common factor.

Rewrite the expression.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = (x - 7) + 5 {({(x - 7)}^{\frac{1}{5}})}^{4} \cdot 63 + 10 {({(x - 7)}^{\frac{1}{5}})}^{3} \cdot 63^{2} + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Simplify.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 5 {({(x - 7)}^{\frac{1}{5}})}^{4} \cdot 63 + 10 {({(x - 7)}^{\frac{1}{5}})}^{3} \cdot 63^{2} + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply the exponents in ${({(x - 7)}^{\frac{1}{5}})}^{4}$ .

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

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 5 {(x - 7)}^{\frac{1}{5} \cdot 4} \cdot 63 + 10 {({(x - 7)}^{\frac{1}{5}})}^{3} \cdot 63^{2} + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Combine $\frac{1}{5}$ and $4$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 5 {(x - 7)}^{\frac{4}{5}} \cdot 63 + 10 {({(x - 7)}^{\frac{1}{5}})}^{3} \cdot 63^{2} + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply $63$ by $5$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 10 {({(x - 7)}^{\frac{1}{5}})}^{3} \cdot 63^{2} + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply the exponents in ${({(x - 7)}^{\frac{1}{5}})}^{3}$ .

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

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 10 {(x - 7)}^{\frac{1}{5} \cdot 3} \cdot 63^{2} + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Combine $\frac{1}{5}$ and $3$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 10 {(x - 7)}^{\frac{3}{5}} \cdot 63^{2} + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Raise $63$ to the power of $2$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 10 {(x - 7)}^{\frac{3}{5}} \cdot 3969 + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply $3969$ by $10$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply the exponents in ${({(x - 7)}^{\frac{1}{5}})}^{2}$ .

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

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 10 {(x - 7)}^{\frac{1}{5} \cdot 2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Combine $\frac{1}{5}$ and $2$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 10 {(x - 7)}^{\frac{2}{5}} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Raise $63$ to the power of $3$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 10 {(x - 7)}^{\frac{2}{5}} \cdot 250047 + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply $250047$ by $10$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Raise $63$ to the power of $4$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 15752961 + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply $15752961$ by $5$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Raise $63$ to the power of $5$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436543 - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Add $- 7$ and $992436543$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

To write $9$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9 \cdot \frac{7}{7})}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Combine $9$ and $\frac{7}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + \frac{9 \cdot 7}{7})}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Combine the numerators over the common denominator.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}} + 9 \cdot 7}{7})}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply $9$ by $7$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7})}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Apply the product rule to $\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 756315 \frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{4}}{7^{4}} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

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

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 756315 \frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{4}}{2401} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Cancel the common factor of $2401$ .

Factor $2401$ out of $- 756315$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 + 2401 (- 315) (\frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{4}}{2401}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Cancel the common factor.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 + 2401 \cdot (- 315 \frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{4}}{2401}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Rewrite the expression.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {({(x - 7)}^{\frac{1}{5}} + 63)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Use the Binomial Theorem.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({({(x - 7)}^{\frac{1}{5}})}^{4} + 4 {({(x - 7)}^{\frac{1}{5}})}^{3} \cdot 63 + 6 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{2} + 4 {(x - 7)}^{\frac{1}{5}} \cdot 63^{3} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Simplify each term.

Multiply the exponents in ${({(x - 7)}^{\frac{1}{5}})}^{4}$ .

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

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{1}{5} \cdot 4} + 4 {({(x - 7)}^{\frac{1}{5}})}^{3} \cdot 63 + 6 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{2} + 4 {(x - 7)}^{\frac{1}{5}} \cdot 63^{3} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Combine $\frac{1}{5}$ and $4$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 4 {({(x - 7)}^{\frac{1}{5}})}^{3} \cdot 63 + 6 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{2} + 4 {(x - 7)}^{\frac{1}{5}} \cdot 63^{3} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply the exponents in ${({(x - 7)}^{\frac{1}{5}})}^{3}$ .

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

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 4 {(x - 7)}^{\frac{1}{5} \cdot 3} \cdot 63 + 6 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{2} + 4 {(x - 7)}^{\frac{1}{5}} \cdot 63^{3} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Combine $\frac{1}{5}$ and $3$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 4 {(x - 7)}^{\frac{3}{5}} \cdot 63 + 6 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{2} + 4 {(x - 7)}^{\frac{1}{5}} \cdot 63^{3} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply $63$ by $4$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 252 {(x - 7)}^{\frac{3}{5}} + 6 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{2} + 4 {(x - 7)}^{\frac{1}{5}} \cdot 63^{3} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply the exponents in ${({(x - 7)}^{\frac{1}{5}})}^{2}$ .

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

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 252 {(x - 7)}^{\frac{3}{5}} + 6 {(x - 7)}^{\frac{1}{5} \cdot 2} \cdot 63^{2} + 4 {(x - 7)}^{\frac{1}{5}} \cdot 63^{3} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Combine $\frac{1}{5}$ and $2$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 252 {(x - 7)}^{\frac{3}{5}} + 6 {(x - 7)}^{\frac{2}{5}} \cdot 63^{2} + 4 {(x - 7)}^{\frac{1}{5}} \cdot 63^{3} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Raise $63$ to the power of $2$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 252 {(x - 7)}^{\frac{3}{5}} + 6 {(x - 7)}^{\frac{2}{5}} \cdot 3969 + 4 {(x - 7)}^{\frac{1}{5}} \cdot 63^{3} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply $3969$ by $6$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 252 {(x - 7)}^{\frac{3}{5}} + 23814 {(x - 7)}^{\frac{2}{5}} + 4 {(x - 7)}^{\frac{1}{5}} \cdot 63^{3} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Raise $63$ to the power of $3$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 252 {(x - 7)}^{\frac{3}{5}} + 23814 {(x - 7)}^{\frac{2}{5}} + 4 {(x - 7)}^{\frac{1}{5}} \cdot 250047 + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply $250047$ by $4$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 252 {(x - 7)}^{\frac{3}{5}} + 23814 {(x - 7)}^{\frac{2}{5}} + 1000188 {(x - 7)}^{\frac{1}{5}} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Raise $63$ to the power of $4$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 252 {(x - 7)}^{\frac{3}{5}} + 23814 {(x - 7)}^{\frac{2}{5}} + 1000188 {(x - 7)}^{\frac{1}{5}} + 15752961) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Apply the distributive property.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 315 (252 {(x - 7)}^{\frac{3}{5}}) - 315 (23814 {(x - 7)}^{\frac{2}{5}}) - 315 (1000188 {(x - 7)}^{\frac{1}{5}}) - 315 \cdot 15752961 + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Simplify.

Multiply $252$ by $- 315$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 315 (23814 {(x - 7)}^{\frac{2}{5}}) - 315 (1000188 {(x - 7)}^{\frac{1}{5}}) - 315 \cdot 15752961 + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply $23814$ by $- 315$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315 (1000188 {(x - 7)}^{\frac{1}{5}}) - 315 \cdot 15752961 + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply $1000188$ by $- 315$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 315 \cdot 15752961 + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply $- 315$ by $15752961$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

To write $9$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9 \cdot \frac{7}{7})}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Combine $9$ and $\frac{7}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + \frac{9 \cdot 7}{7})}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Combine the numerators over the common denominator.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}} + 9 \cdot 7}{7})}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply $9$ by $7$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7})}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Apply the product rule to $\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 13613670 (\frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{3}}{7^{3}}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

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

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 13613670 (\frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{3}}{343}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Cancel the common factor of $343$ .

Factor $343$ out of $13613670$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 343 (39690) (\frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{3}}{343}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Cancel the common factor.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 343 \cdot (39690 (\frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{3}}{343})) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Rewrite the expression.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {({(x - 7)}^{\frac{1}{5}} + 63)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Use the Binomial Theorem.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 ({({(x - 7)}^{\frac{1}{5}})}^{3} + 3 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63 + 3 {(x - 7)}^{\frac{1}{5}} \cdot 63^{2} + 63^{3}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Simplify each term.

Multiply the exponents in ${({(x - 7)}^{\frac{1}{5}})}^{3}$ .

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

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 ({(x - 7)}^{\frac{1}{5} \cdot 3} + 3 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63 + 3 {(x - 7)}^{\frac{1}{5}} \cdot 63^{2} + 63^{3}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Combine $\frac{1}{5}$ and $3$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 ({(x - 7)}^{\frac{3}{5}} + 3 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63 + 3 {(x - 7)}^{\frac{1}{5}} \cdot 63^{2} + 63^{3}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply the exponents in ${({(x - 7)}^{\frac{1}{5}})}^{2}$ .

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

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 ({(x - 7)}^{\frac{3}{5}} + 3 {(x - 7)}^{\frac{1}{5} \cdot 2} \cdot 63 + 3 {(x - 7)}^{\frac{1}{5}} \cdot 63^{2} + 63^{3}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Combine $\frac{1}{5}$ and $2$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 ({(x - 7)}^{\frac{3}{5}} + 3 {(x - 7)}^{\frac{2}{5}} \cdot 63 + 3 {(x - 7)}^{\frac{1}{5}} \cdot 63^{2} + 63^{3}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply $63$ by $3$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 ({(x - 7)}^{\frac{3}{5}} + 189 {(x - 7)}^{\frac{2}{5}} + 3 {(x - 7)}^{\frac{1}{5}} \cdot 63^{2} + 63^{3}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Raise $63$ to the power of $2$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 ({(x - 7)}^{\frac{3}{5}} + 189 {(x - 7)}^{\frac{2}{5}} + 3 {(x - 7)}^{\frac{1}{5}} \cdot 3969 + 63^{3}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply $3969$ by $3$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 ({(x - 7)}^{\frac{3}{5}} + 189 {(x - 7)}^{\frac{2}{5}} + 11907 {(x - 7)}^{\frac{1}{5}} + 63^{3}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Raise $63$ to the power of $3$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 ({(x - 7)}^{\frac{3}{5}} + 189 {(x - 7)}^{\frac{2}{5}} + 11907 {(x - 7)}^{\frac{1}{5}} + 250047) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Apply the distributive property.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 39690 (189 {(x - 7)}^{\frac{2}{5}}) + 39690 (11907 {(x - 7)}^{\frac{1}{5}}) + 39690 \cdot 250047 - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Simplify.

Multiply $189$ by $39690$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 39690 (11907 {(x - 7)}^{\frac{1}{5}}) + 39690 \cdot 250047 - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply $11907$ by $39690$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 39690 \cdot 250047 - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply $39690$ by $250047$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

To write $9$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9 \cdot \frac{7}{7})}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Combine $9$ and $\frac{7}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + \frac{9 \cdot 7}{7})}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Combine the numerators over the common denominator.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}} + 9 \cdot 7}{7})}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply $9$ by $7$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7})}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Apply the product rule to $\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 122523030 \frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{2}}{7^{2}} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Raise $7$ to the power of $2$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 122523030 \frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{2}}{49} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Cancel the common factor of $49$ .

Factor $49$ out of $- 122523030$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 + 49 (- 2500470) (\frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{2}}{49}) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Cancel the common factor.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 + 49 \cdot (- 2500470 \frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{2}}{49}) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Rewrite the expression.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {({(x - 7)}^{\frac{1}{5}} + 63)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Rewrite ${({(x - 7)}^{\frac{1}{5}} + 63)}^{2}$ as $({(x - 7)}^{\frac{1}{5}} + 63) ({(x - 7)}^{\frac{1}{5}} + 63)$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 (({(x - 7)}^{\frac{1}{5}} + 63) ({(x - 7)}^{\frac{1}{5}} + 63)) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Expand $({(x - 7)}^{\frac{1}{5}} + 63) ({(x - 7)}^{\frac{1}{5}} + 63)$ using the FOIL Method.

Apply the distributive property.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 ({(x - 7)}^{\frac{1}{5}} ({(x - 7)}^{\frac{1}{5}} + 63) + 63 ({(x - 7)}^{\frac{1}{5}} + 63)) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Apply the distributive property.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 ({(x - 7)}^{\frac{1}{5}} {(x - 7)}^{\frac{1}{5}} + {(x - 7)}^{\frac{1}{5}} \cdot 63 + 63 ({(x - 7)}^{\frac{1}{5}} + 63)) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Apply the distributive property.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 ({(x - 7)}^{\frac{1}{5}} {(x - 7)}^{\frac{1}{5}} + {(x - 7)}^{\frac{1}{5}} \cdot 63 + 63 {(x - 7)}^{\frac{1}{5}} + 63 \cdot 63) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Simplify and combine like terms.

Simplify each term.

Multiply ${(x - 7)}^{\frac{1}{5}}$ by ${(x - 7)}^{\frac{1}{5}}$ by adding the exponents.

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

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 ({(x - 7)}^{\frac{1}{5} + \frac{1}{5}} + {(x - 7)}^{\frac{1}{5}} \cdot 63 + 63 {(x - 7)}^{\frac{1}{5}} + 63 \cdot 63) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Combine the numerators over the common denominator.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 ({(x - 7)}^{\frac{1 + 1}{5}} + {(x - 7)}^{\frac{1}{5}} \cdot 63 + 63 {(x - 7)}^{\frac{1}{5}} + 63 \cdot 63) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Add $1$ and $1$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 ({(x - 7)}^{\frac{2}{5}} + {(x - 7)}^{\frac{1}{5}} \cdot 63 + 63 {(x - 7)}^{\frac{1}{5}} + 63 \cdot 63) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Move $63$ to the left of ${(x - 7)}^{\frac{1}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 ({(x - 7)}^{\frac{2}{5}} + 63 \cdot {(x - 7)}^{\frac{1}{5}} + 63 {(x - 7)}^{\frac{1}{5}} + 63 \cdot 63) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply $63$ by $63$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 ({(x - 7)}^{\frac{2}{5}} + 63 {(x - 7)}^{\frac{1}{5}} + 63 {(x - 7)}^{\frac{1}{5}} + 3969) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Add $63 {(x - 7)}^{\frac{1}{5}}$ and $63 {(x - 7)}^{\frac{1}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 ({(x - 7)}^{\frac{2}{5}} + 126 {(x - 7)}^{\frac{1}{5}} + 3969) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Apply the distributive property.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 2500470 (126 {(x - 7)}^{\frac{1}{5}}) - 2500470 \cdot 3969 + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Simplify.

Multiply $126$ by $- 2500470$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 2500470 \cdot 3969 + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Multiply $- 2500470$ by $3969$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

To write $9$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9 \cdot \frac{7}{7}) - 992436536$

Combine $9$ and $\frac{7}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + \frac{9 \cdot 7}{7}) - 992436536$

Combine the numerators over the common denominator.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}} + 9 \cdot 7}{7}) - 992436536$

Multiply $9$ by $7$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7}) - 992436536$

Cancel the common factor of $7$ .

Factor $7$ out of $551353635$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 7 (78764805) (\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7}) - 992436536$

Cancel the common factor.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 7 \cdot (78764805 (\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7})) - 992436536$

Rewrite the expression.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 78764805 ({(x - 7)}^{\frac{1}{5}} + 63) - 992436536$

Apply the distributive property.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 78764805 {(x - 7)}^{\frac{1}{5}} + 78764805 \cdot 63 - 992436536$

Multiply $78764805$ by $63$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 78764805 {(x - 7)}^{\frac{1}{5}} + 4962182715 - 992436536$

Simplify by adding terms.

Combine the opposite terms in $x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 78764805 {(x - 7)}^{\frac{1}{5}} + 4962182715 - 992436536$ .

Subtract $315 {(x - 7)}^{\frac{4}{5}}$ from $315 {(x - 7)}^{\frac{4}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 + 0 - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 78764805 {(x - 7)}^{\frac{1}{5}} + 4962182715 - 992436536$

Add $x + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536$ and $0$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 78764805 {(x - 7)}^{\frac{1}{5}} + 4962182715 - 992436536$

Add $- 7501410 {(x - 7)}^{\frac{2}{5}}$ and $7501410 {(x - 7)}^{\frac{2}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} + 0 - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 78764805 {(x - 7)}^{\frac{1}{5}} + 4962182715 - 992436536$

Add $x + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}}$ and $0$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 78764805 {(x - 7)}^{\frac{1}{5}} + 4962182715 - 992436536$

Subtract $2500470 {(x - 7)}^{\frac{2}{5}}$ from $2500470 {(x - 7)}^{\frac{2}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 + 0 - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 78764805 {(x - 7)}^{\frac{1}{5}} + 4962182715 - 992436536$

Add $x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430$ and $0$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 78764805 {(x - 7)}^{\frac{1}{5}} + 4962182715 - 992436536$

Subtract $9924365430$ from $9924365430$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 0 - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 4962182715 - 992436536$

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 4962182715 - 992436536$

Add $- 4962182715$ and $4962182715$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 0 - 992436536$

Add $x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$ and $0$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} - 992436536$

Subtract $992436536$ from $992436536$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 0 - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$

Add $x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$ and $0$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$

Subtract $79380 {(x - 7)}^{\frac{3}{5}}$ from $39690 {(x - 7)}^{\frac{3}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 78764805 {(x - 7)}^{\frac{1}{5}} - 39690 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$

Combine the opposite terms in $x + 78764805 {(x - 7)}^{\frac{1}{5}} - 39690 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$ .

Add $- 39690 {(x - 7)}^{\frac{3}{5}}$ and $39690 {(x - 7)}^{\frac{3}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 78764805 {(x - 7)}^{\frac{1}{5}} + 0 - 315059220 {(x - 7)}^{\frac{1}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$

Add $x + 78764805 {(x - 7)}^{\frac{1}{5}}$ and $0$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 78764805 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$

Subtract $315059220 {(x - 7)}^{\frac{1}{5}}$ from $78764805 {(x - 7)}^{\frac{1}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 236294415 {(x - 7)}^{\frac{1}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$

Add $- 236294415 {(x - 7)}^{\frac{1}{5}}$ and $472588830 {(x - 7)}^{\frac{1}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 236294415 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$

Subtract $315059220 {(x - 7)}^{\frac{1}{5}}$ from $236294415 {(x - 7)}^{\frac{1}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 78764805 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$

Combine the opposite terms in $x - 78764805 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$ .

Add $- 78764805 {(x - 7)}^{\frac{1}{5}}$ and $78764805 {(x - 7)}^{\frac{1}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 0$

Add $x$ and $0$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x$

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

Set up the composite result function.

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

Evaluate $f (16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436536)$ by substituting in the value of $f^{- 1}$ into $f$ .

$f (16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436536) = \frac{{((16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436536) - 7)}^{\frac{1}{5}}}{7} + 9$

Subtract $7$ from $- 992436536$ .

$f (16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436536) = \frac{{(16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436543)}^{\frac{1}{5}}}{7} + 9$

To write $9$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

Combine $9$ and $\frac{7}{7}$ .

Combine the numerators over the common denominator.

Multiply $9$ by $7$ .

Since $f^{- 1} (f (x)) = x$ and $f (f^{- 1} (x)) = x$ , then $f^{- 1} (x) = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436536$ is the inverse of $f (x) = \frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9$ .

$f^{- 1} (x) = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436536$

Find the Inverse f(x)=((x-7)^(1/5))/7+9

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