Let $a,b\in\Bbb{N}$ such that $\gcd(a,b)=1$ and $n,r\in\Bbb{N}^*$. If $ab=n^r$ then there exists $k,l\in\Bbb{N}$ such that $a=k^r$ and $b=l^r$.
If a product of relatively prime integers is an $n$th power, then each is an $n$th power