Prove if $a^n|b^n$ then $a|b$

Question

So assume that $a^n|b^n$ then $b^n=a^n(x)$ for some integer $x$ taking the nth root of both sides you get $b=a(x^{\frac{1}{n}})$. Now I'm not sure if this is ok since $x^{\frac{1}{n}}$ is not always an integer. But it seems like it should always work so I"m not sure if this is the correct approach.