Prove: $f(x)^{p^k}\equiv f\left(x^{p^k}\right)\bmod p$

Prove: $f(x)^{p^k}\equiv f\left(x^{p^k}\right)\bmod p$

$p$ is a prime number, $k$ is an positive integer.
Prove: $f(x)^{p^k}\equiv f\left(x^{p^k}\right)\bmod p$