Find the Inverse f(x)=(4x)^(5/3)

Rewrite the equation as ${\displaystyle {\left(4y\right)}^{\frac{5}{3}}=x}$.

Raise each side of the equation to the power of ${\displaystyle \frac{3}{5}}$ to eliminate the fractional exponent on the left side.

Simplify the left side.

Divide each term in ${\displaystyle 4y=x^{\frac{3}{5}}}$ by ${\displaystyle 4}$ and simplify.

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

Evaluate ${\displaystyle f^{-1}\left(f\left(x\right)\right)}$.

Evaluate ${\displaystyle f\left(f^{-1}\left(x\right)\right)}$.

Since ${\displaystyle f^{-1}\left(f\left(x\right)\right)=x}$ and ${\displaystyle f\left(f^{-1}\left(x\right)\right)=x}$, then ${\displaystyle f^{-1}\left(x\right)=\frac{x^{\frac{3}{5}}}{4}}$ is the inverse of ${\displaystyle f\left(x\right)={\left(4x\right)}^{\frac{5}{3}}}$.