Inverse Powers and Radical Functions

$$\text{True or False}$$

=== If $f(x)=ax^b$ and $f^{-1}(x)=(\frac1a)^{\frac1b}x^{\frac1b}$ where $a$ and $b$ are nonzero real numbers, then $f(x)f^{-1}(x)$ is also a power function.