elementary number theory - Suppose $a, b$ and $n$ are positive integers. Prove that $a^n$ divides $b^n$ if and only if $a$ divides $b$.

I think prime factorization is needed for this question:

Suppose $a$, $b$ and $n$ are positive integers. Prove that $a^n$ divides $b^n$ if and only if a divides $b$.