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

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

Step 1

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

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

Step 2

Interchange the variables.

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

Step 3

Solve for $y$ .

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

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

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

Subtract $7$ from both sides of the equation.

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

Add $x$ to both sides of the equation.

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

Multiply both sides of the equation by $9$ .

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

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Simplify $9 (- 7 + x)$ .

Apply the distributive property.

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

Multiply $9$ by $- 7$ .

$y^{\frac{1}{5}} = - 63 + 9 x$

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

${(y^{\frac{1}{5}})}^{5} = {(- 63 + 9 x)}^{5}$

Simplify the exponent.

Simplify the left side.

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

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

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

$y^{\frac{1}{5} \cdot 5} = {(- 63 + 9 x)}^{5}$

Cancel the common factor of $5$ .

Cancel the common factor.

$y^{\frac{1}{5} \cdot 5} = {(- 63 + 9 x)}^{5}$

Rewrite the expression.

$y^{1} = {(- 63 + 9 x)}^{5}$

Simplify.

$y = {(- 63 + 9 x)}^{5}$

Simplify the right side.

Simplify ${(- 63 + 9 x)}^{5}$ .

Use the Binomial Theorem.

$y = {(- 63)}^{5} + 5 {(- 63)}^{4} (9 x) + 10 {(- 63)}^{3} {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Simplify each term.

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

$y = - 992436543 + 5 {(- 63)}^{4} (9 x) + 10 {(- 63)}^{3} {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

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

$y = - 992436543 + 5 \cdot 15752961 (9 x) + 10 {(- 63)}^{3} {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Multiply $5$ by $15752961$ .

$y = - 992436543 + 78764805 (9 x) + 10 {(- 63)}^{3} {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Multiply $9$ by $78764805$ .

$y = - 992436543 + 708883245 x + 10 {(- 63)}^{3} {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

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

$y = - 992436543 + 708883245 x + 10 \cdot - 250047 {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Multiply $10$ by $- 250047$ .

$y = - 992436543 + 708883245 x - 2500470 {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Apply the product rule to $9 x$ .

$y = - 992436543 + 708883245 x - 2500470 (9^{2} x^{2}) + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Raise $9$ to the power of $2$ .

$y = - 992436543 + 708883245 x - 2500470 (81 x^{2}) + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Multiply $81$ by $- 2500470$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

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

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 10 \cdot 3969 {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Multiply $10$ by $3969$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 39690 {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Apply the product rule to $9 x$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 39690 (9^{3} x^{3}) + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Raise $9$ to the power of $3$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 39690 (729 x^{3}) + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Multiply $729$ by $39690$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Multiply $5$ by $- 63$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 315 {(9 x)}^{4} + {(9 x)}^{5}$

Apply the product rule to $9 x$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 315 (9^{4} x^{4}) + {(9 x)}^{5}$

Raise $9$ to the power of $4$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 315 (6561 x^{4}) + {(9 x)}^{5}$

Multiply $6561$ by $- 315$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 2066715 x^{4} + {(9 x)}^{5}$

Apply the product rule to $9 x$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 2066715 x^{4} + 9^{5} x^{5}$

Raise $9$ to the power of $5$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 2066715 x^{4} + 59049 x^{5}$

Simplify $- 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 2066715 x^{4} + 59049 x^{5}$ .

Move $- 992436543$ .

$y = 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 2066715 x^{4} + 59049 x^{5} - 992436543$

Move $708883245 x$ .

$y = - 202538070 x^{2} + 28934010 x^{3} - 2066715 x^{4} + 59049 x^{5} + 708883245 x - 992436543$

Move $- 202538070 x^{2}$ .

$y = 28934010 x^{3} - 2066715 x^{4} + 59049 x^{5} - 202538070 x^{2} + 708883245 x - 992436543$

Move $28934010 x^{3}$ .

$y = - 2066715 x^{4} + 59049 x^{5} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543$

Reorder $- 2066715 x^{4}$ and $59049 x^{5}$ .

$y = 59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543$

Step 4

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

$f^{- 1} (x) = 59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543$

Step 5

Verify if $f^{- 1} (x) = 59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543$ is the inverse of $f (x) = \frac{x^{\frac{1}{5}}}{9} + 7$ .

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{5} - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Simplify each term.

Use the Binomial Theorem.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 ({(\frac{x^{\frac{1}{5}}}{9})}^{5} + 5 {(\frac{x^{\frac{1}{5}}}{9})}^{4} \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Simplify each term.

Apply the product rule to $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{{(x^{\frac{1}{5}})}^{5}}{9^{5}} + 5 {(\frac{x^{\frac{1}{5}}}{9})}^{4} \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Simplify the numerator.

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

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x^{\frac{1}{5} \cdot 5}}{9^{5}} + 5 {(\frac{x^{\frac{1}{5}}}{9})}^{4} \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor of $5$ .

Cancel the common factor.

Rewrite the expression.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{9^{5}} + 5 {(\frac{x^{\frac{1}{5}}}{9})}^{4} \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Simplify.

Raise $9$ to the power of $5$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + 5 {(\frac{x^{\frac{1}{5}}}{9})}^{4} \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Apply the product rule to $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + 5 (\frac{{(x^{\frac{1}{5}})}^{4}}{9^{4}}) \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + 5 (\frac{x^{\frac{1}{5} \cdot 4}}{9^{4}}) \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + 5 (\frac{x^{\frac{4}{5}}}{9^{4}}) \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Raise $9$ to the power of $4$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + 5 (\frac{x^{\frac{4}{5}}}{6561}) \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Combine $5$ and $\frac{x^{\frac{4}{5}}}{6561}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{5 x^{\frac{4}{5}}}{6561} \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $\frac{5 x^{\frac{4}{5}}}{6561} \cdot 7$ .

Combine $\frac{5 x^{\frac{4}{5}}}{6561}$ and $7$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{5 x^{\frac{4}{5}} \cdot 7}{6561} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $7$ by $5$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Apply the product rule to $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + 10 (\frac{{(x^{\frac{1}{5}})}^{3}}{9^{3}}) \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + 10 (\frac{x^{\frac{1}{5} \cdot 3}}{9^{3}}) \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + 10 (\frac{x^{\frac{3}{5}}}{9^{3}}) \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Raise $9$ to the power of $3$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + 10 (\frac{x^{\frac{3}{5}}}{729}) \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Combine $10$ and $\frac{x^{\frac{3}{5}}}{729}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{10 x^{\frac{3}{5}}}{729} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{10 x^{\frac{3}{5}}}{729} \cdot 49 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $\frac{10 x^{\frac{3}{5}}}{729} \cdot 49$ .

Combine $\frac{10 x^{\frac{3}{5}}}{729}$ and $49$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{10 x^{\frac{3}{5}} \cdot 49}{729} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $49$ by $10$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Apply the product rule to $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + 10 (\frac{{(x^{\frac{1}{5}})}^{2}}{9^{2}}) \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + 10 (\frac{x^{\frac{1}{5} \cdot 2}}{9^{2}}) \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + 10 (\frac{x^{\frac{2}{5}}}{9^{2}}) \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Raise $9$ to the power of $2$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + 10 (\frac{x^{\frac{2}{5}}}{81}) \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Combine $10$ and $\frac{x^{\frac{2}{5}}}{81}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{10 x^{\frac{2}{5}}}{81} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{10 x^{\frac{2}{5}}}{81} \cdot 343 + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $\frac{10 x^{\frac{2}{5}}}{81} \cdot 343$ .

Combine $\frac{10 x^{\frac{2}{5}}}{81}$ and $343$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{10 x^{\frac{2}{5}} \cdot 343}{81} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $343$ by $10$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{3430 x^{\frac{2}{5}}}{81} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Combine $5$ and $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{3430 x^{\frac{2}{5}}}{81} + \frac{5 x^{\frac{1}{5}}}{9} \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{3430 x^{\frac{2}{5}}}{81} + \frac{5 x^{\frac{1}{5}}}{9} \cdot 2401 + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $\frac{5 x^{\frac{1}{5}}}{9} \cdot 2401$ .

Combine $\frac{5 x^{\frac{1}{5}}}{9}$ and $2401$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{3430 x^{\frac{2}{5}}}{81} + \frac{5 x^{\frac{1}{5}} \cdot 2401}{9} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $2401$ by $5$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{3430 x^{\frac{2}{5}}}{81} + \frac{12005 x^{\frac{1}{5}}}{9} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{3430 x^{\frac{2}{5}}}{81} + \frac{12005 x^{\frac{1}{5}}}{9} + 16807) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Apply the distributive property.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049}) + 59049 (\frac{35 x^{\frac{4}{5}}}{6561}) + 59049 (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Simplify.

Cancel the common factor of $59049$ .

Cancel the common factor.

Rewrite the expression.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 59049 (\frac{35 x^{\frac{4}{5}}}{6561}) + 59049 (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor of $6561$ .

Factor $6561$ out of $59049$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 6561 (9) (\frac{35 x^{\frac{4}{5}}}{6561}) + 59049 (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 6561 \cdot (9 (\frac{35 x^{\frac{4}{5}}}{6561})) + 59049 (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Rewrite the expression.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 9 (35 x^{\frac{4}{5}}) + 59049 (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $35$ by $9$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 59049 (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor of $729$ .

Factor $729$ out of $59049$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 729 (81) (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 729 \cdot (81 (\frac{490 x^{\frac{3}{5}}}{729})) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Rewrite the expression.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 81 (490 x^{\frac{3}{5}}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $490$ by $81$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor of $81$ .

Factor $81$ out of $59049$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 81 (729) (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 81 \cdot (729 (\frac{3430 x^{\frac{2}{5}}}{81})) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Rewrite the expression.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 729 (3430 x^{\frac{2}{5}}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $3430$ by $729$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor of $9$ .

Factor $9$ out of $59049$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 9 (6561) (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 9 \cdot (6561 (\frac{12005 x^{\frac{1}{5}}}{9})) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Rewrite the expression.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 6561 (12005 x^{\frac{1}{5}}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $12005$ by $6561$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $59049$ by $16807$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Use the Binomial Theorem.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 ({(\frac{x^{\frac{1}{5}}}{9})}^{4} + 4 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Simplify each term.

Apply the product rule to $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{{(x^{\frac{1}{5}})}^{4}}{9^{4}} + 4 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{1}{5} \cdot 4}}{9^{4}} + 4 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{9^{4}} + 4 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Raise $9$ to the power of $4$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + 4 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Apply the product rule to $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + 4 (\frac{{(x^{\frac{1}{5}})}^{3}}{9^{3}}) \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + 4 (\frac{x^{\frac{1}{5} \cdot 3}}{9^{3}}) \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + 4 (\frac{x^{\frac{3}{5}}}{9^{3}}) \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Raise $9$ to the power of $3$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + 4 (\frac{x^{\frac{3}{5}}}{729}) \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Combine $4$ and $\frac{x^{\frac{3}{5}}}{729}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{4 x^{\frac{3}{5}}}{729} \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $\frac{4 x^{\frac{3}{5}}}{729} \cdot 7$ .

Combine $\frac{4 x^{\frac{3}{5}}}{729}$ and $7$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{4 x^{\frac{3}{5}} \cdot 7}{729} + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $7$ by $4$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Apply the product rule to $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 6 (\frac{{(x^{\frac{1}{5}})}^{2}}{9^{2}}) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 6 (\frac{x^{\frac{1}{5} \cdot 2}}{9^{2}}) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 6 (\frac{x^{\frac{2}{5}}}{9^{2}}) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Raise $9$ to the power of $2$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 6 (\frac{x^{\frac{2}{5}}}{81}) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 3 (2) (\frac{x^{\frac{2}{5}}}{81}) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Factor $3$ out of $81$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 3 \cdot (2 (\frac{x^{\frac{2}{5}}}{3 \cdot 27})) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 3 \cdot (2 (\frac{x^{\frac{2}{5}}}{3 \cdot 27})) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Rewrite the expression.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 2 (\frac{x^{\frac{2}{5}}}{27}) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Combine $2$ and $\frac{x^{\frac{2}{5}}}{27}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{2 x^{\frac{2}{5}}}{27} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{2 x^{\frac{2}{5}}}{27} \cdot 49 + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $\frac{2 x^{\frac{2}{5}}}{27} \cdot 49$ .

Combine $\frac{2 x^{\frac{2}{5}}}{27}$ and $49$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{2 x^{\frac{2}{5}} \cdot 49}{27} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $49$ by $2$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{98 x^{\frac{2}{5}}}{27} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Combine $4$ and $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{98 x^{\frac{2}{5}}}{27} + \frac{4 x^{\frac{1}{5}}}{9} \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{98 x^{\frac{2}{5}}}{27} + \frac{4 x^{\frac{1}{5}}}{9} \cdot 343 + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $\frac{4 x^{\frac{1}{5}}}{9} \cdot 343$ .

Combine $\frac{4 x^{\frac{1}{5}}}{9}$ and $343$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{98 x^{\frac{2}{5}}}{27} + \frac{4 x^{\frac{1}{5}} \cdot 343}{9} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $343$ by $4$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{98 x^{\frac{2}{5}}}{27} + \frac{1372 x^{\frac{1}{5}}}{9} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{98 x^{\frac{2}{5}}}{27} + \frac{1372 x^{\frac{1}{5}}}{9} + 2401) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Apply the distributive property.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 \frac{x^{\frac{4}{5}}}{6561} - 2066715 \frac{28 x^{\frac{3}{5}}}{729} - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Simplify.

Cancel the common factor of $6561$ .

Factor $6561$ out of $- 2066715$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 + 6561 (- 315) (\frac{x^{\frac{4}{5}}}{6561}) - 2066715 \frac{28 x^{\frac{3}{5}}}{729} - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 + 6561 \cdot (- 315 \frac{x^{\frac{4}{5}}}{6561}) - 2066715 \frac{28 x^{\frac{3}{5}}}{729} - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Rewrite the expression.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 2066715 \frac{28 x^{\frac{3}{5}}}{729} - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor of $729$ .

Factor $729$ out of $- 2066715$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} + 729 (- 2835) (\frac{28 x^{\frac{3}{5}}}{729}) - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} + 729 \cdot (- 2835 \frac{28 x^{\frac{3}{5}}}{729}) - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Rewrite the expression.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 2835 (28 x^{\frac{3}{5}}) - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $28$ by $- 2835$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor of $27$ .

Factor $27$ out of $- 2066715$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} + 27 (- 76545) (\frac{98 x^{\frac{2}{5}}}{27}) - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} + 27 \cdot (- 76545 \frac{98 x^{\frac{2}{5}}}{27}) - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Rewrite the expression.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 76545 (98 x^{\frac{2}{5}}) - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $98$ by $- 76545$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor of $9$ .

Factor $9$ out of $- 2066715$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} + 9 (- 229635) (\frac{1372 x^{\frac{1}{5}}}{9}) - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} + 9 \cdot (- 229635 \frac{1372 x^{\frac{1}{5}}}{9}) - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Rewrite the expression.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 229635 (1372 x^{\frac{1}{5}}) - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $1372$ by $- 229635$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $- 2066715$ by $2401$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Use the Binomial Theorem.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 ({(\frac{x^{\frac{1}{5}}}{9})}^{3} + 3 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Simplify each term.

Apply the product rule to $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{{(x^{\frac{1}{5}})}^{3}}{9^{3}} + 3 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{1}{5} \cdot 3}}{9^{3}} + 3 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{9^{3}} + 3 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Raise $9$ to the power of $3$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Apply the product rule to $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 (\frac{{(x^{\frac{1}{5}})}^{2}}{9^{2}}) \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 (\frac{x^{\frac{1}{5} \cdot 2}}{9^{2}}) \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 (\frac{x^{\frac{2}{5}}}{9^{2}}) \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Raise $9$ to the power of $2$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 (\frac{x^{\frac{2}{5}}}{81}) \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor of $3$ .

Factor $3$ out of $81$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 (\frac{x^{\frac{2}{5}}}{3 (27)}) \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 (\frac{x^{\frac{2}{5}}}{3 \cdot 27}) \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Rewrite the expression.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{x^{\frac{2}{5}}}{27} \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Combine $\frac{x^{\frac{2}{5}}}{27}$ and $7$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{x^{\frac{2}{5}} \cdot 7}{27} + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Move $7$ to the left of $x^{\frac{2}{5}}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 \cdot x^{\frac{2}{5}}}{27} + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + 3 (\frac{x^{\frac{1}{5}}}{3 (3)}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + 3 (\frac{x^{\frac{1}{5}}}{3 \cdot 3}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Rewrite the expression.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + \frac{x^{\frac{1}{5}}}{3} \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + \frac{x^{\frac{1}{5}}}{3} \cdot 49 + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Combine $\frac{x^{\frac{1}{5}}}{3}$ and $49$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + \frac{x^{\frac{1}{5}} \cdot 49}{3} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Move $49$ to the left of $x^{\frac{1}{5}}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + \frac{49 \cdot x^{\frac{1}{5}}}{3} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + \frac{49 x^{\frac{1}{5}}}{3} + 343) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Apply the distributive property.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729}) + 28934010 (\frac{7 x^{\frac{2}{5}}}{27}) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Simplify.

Cancel the common factor of $729$ .

Factor $729$ out of $28934010$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 729 (39690) (\frac{x^{\frac{3}{5}}}{729}) + 28934010 (\frac{7 x^{\frac{2}{5}}}{27}) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 729 \cdot (39690 (\frac{x^{\frac{3}{5}}}{729})) + 28934010 (\frac{7 x^{\frac{2}{5}}}{27}) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Rewrite the expression.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 28934010 (\frac{7 x^{\frac{2}{5}}}{27}) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor of $27$ .

Factor $27$ out of $28934010$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 27 (1071630) (\frac{7 x^{\frac{2}{5}}}{27}) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 27 \cdot (1071630 (\frac{7 x^{\frac{2}{5}}}{27})) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Rewrite the expression.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 1071630 (7 x^{\frac{2}{5}}) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $7$ by $1071630$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor of $3$ .

Factor $3$ out of $28934010$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 3 (9644670) (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 3 \cdot (9644670 (\frac{49 x^{\frac{1}{5}}}{3})) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Rewrite the expression.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 9644670 (49 x^{\frac{1}{5}}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $49$ by $9644670$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $28934010$ by $343$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Rewrite ${(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2}$ as $(\frac{x^{\frac{1}{5}}}{9} + 7) (\frac{x^{\frac{1}{5}}}{9} + 7)$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 ((\frac{x^{\frac{1}{5}}}{9} + 7) (\frac{x^{\frac{1}{5}}}{9} + 7)) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Expand $(\frac{x^{\frac{1}{5}}}{9} + 7) (\frac{x^{\frac{1}{5}}}{9} + 7)$ using the FOIL Method.

Apply the distributive property.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{1}{5}}}{9} \cdot (\frac{x^{\frac{1}{5}}}{9} + 7) + 7 (\frac{x^{\frac{1}{5}}}{9} + 7)) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Apply the distributive property.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{1}{5}}}{9} \cdot \frac{x^{\frac{1}{5}}}{9} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9} + 7)) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Apply the distributive property.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{1}{5}}}{9} \cdot \frac{x^{\frac{1}{5}}}{9} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Simplify and combine like terms.

Simplify each term.

Combine.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{1}{5}} x^{\frac{1}{5}}}{9 \cdot 9} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $x^{\frac{1}{5}}$ by $x^{\frac{1}{5}}$ by adding the exponents.

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{1}{5} + \frac{1}{5}}}{9 \cdot 9} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Combine the numerators over the common denominator.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{1 + 1}{5}}}{9 \cdot 9} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Add $1$ and $1$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{9 \cdot 9} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $9$ by $9$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Combine $\frac{x^{\frac{1}{5}}}{9}$ and $7$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{x^{\frac{1}{5}} \cdot 7}{9} + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{7 \cdot x^{\frac{1}{5}}}{9} + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Combine $7$ and $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{7 x^{\frac{1}{5}}}{9} + \frac{7 x^{\frac{1}{5}}}{9} + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $7$ by $7$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{7 x^{\frac{1}{5}}}{9} + \frac{7 x^{\frac{1}{5}}}{9} + 49) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Add $\frac{7 x^{\frac{1}{5}}}{9}$ and $\frac{7 x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + 2 (\frac{7 x^{\frac{1}{5}}}{9}) + 49) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $2 \frac{7 x^{\frac{1}{5}}}{9}$ .

Combine $2$ and $\frac{7 x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{2 (7 x^{\frac{1}{5}})}{9} + 49) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $7$ by $2$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{14 x^{\frac{1}{5}}}{9} + 49) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Apply the distributive property.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 \frac{x^{\frac{2}{5}}}{81} - 202538070 \frac{14 x^{\frac{1}{5}}}{9} - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Simplify.

Cancel the common factor of $81$ .

Factor $81$ out of $- 202538070$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 + 81 (- 2500470) (\frac{x^{\frac{2}{5}}}{81}) - 202538070 \frac{14 x^{\frac{1}{5}}}{9} - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 + 81 \cdot (- 2500470 \frac{x^{\frac{2}{5}}}{81}) - 202538070 \frac{14 x^{\frac{1}{5}}}{9} - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Rewrite the expression.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 202538070 \frac{14 x^{\frac{1}{5}}}{9} - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor of $9$ .

Factor $9$ out of $- 202538070$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} + 9 (- 22504230) (\frac{14 x^{\frac{1}{5}}}{9}) - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Cancel the common factor.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} + 9 \cdot (- 22504230 \frac{14 x^{\frac{1}{5}}}{9}) - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Rewrite the expression.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 22504230 (14 x^{\frac{1}{5}}) - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $14$ by $- 22504230$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Multiply $- 202538070$ by $49$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Apply the distributive property.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 708883245 (\frac{x^{\frac{1}{5}}}{9}) + 708883245 \cdot 7 - 992436543$

Cancel the common factor of $9$ .

Factor $9$ out of $708883245$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 9 (78764805) (\frac{x^{\frac{1}{5}}}{9}) + 708883245 \cdot 7 - 992436543$

Cancel the common factor.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 9 \cdot (78764805 (\frac{x^{\frac{1}{5}}}{9})) + 708883245 \cdot 7 - 992436543$

Rewrite the expression.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 708883245 \cdot 7 - 992436543$

Multiply $708883245$ by $7$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

Simplify by adding terms.

Combine the opposite terms in $x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$ .

Subtract $315 x^{\frac{4}{5}}$ from $315 x^{\frac{4}{5}}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 + 0 - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

Add $x + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543$ and $0$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 0 + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

Add $x + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}}$ and $0$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

Subtract $2500470 x^{\frac{2}{5}}$ from $2500470 x^{\frac{2}{5}}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 + 0 - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

Add $x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430$ and $0$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

Subtract $9924365430$ from $9924365430$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 0 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

Add $- 4962182715$ and $4962182715$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}} + 0 - 992436543$

Add $x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$ and $0$ .

Subtract $992436543$ from $992436543$ .

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

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

Subtract $79380 x^{\frac{3}{5}}$ from $39690 x^{\frac{3}{5}}$ .

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

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

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

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

Add $x + 78764805 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}}$ and $0$ .

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

Subtract $315059220 x^{\frac{1}{5}}$ from $78764805 x^{\frac{1}{5}}$ .

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

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

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

Subtract $315059220 x^{\frac{1}{5}}$ from $236294415 x^{\frac{1}{5}}$ .

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

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

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

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

Add $x$ and $0$ .

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

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

Set up the composite result function.

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

Evaluate $f (59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543)$ by substituting in the value of $f^{- 1}$ into $f$ .

$f (59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543) = \frac{{(59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543)}^{\frac{1}{5}}}{9} + 7$

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

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

Combine the numerators over the common denominator.

Multiply $7$ by $9$ .

Since $f^{- 1} (f (x)) = x$ and $f (f^{- 1} (x)) = x$ , then $f^{- 1} (x) = 59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543$ is the inverse of $f (x) = \frac{x^{\frac{1}{5}}}{9} + 7$ .

$f^{- 1} (x) = 59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543$

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

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