I get stuck with this question :
Let $g$ be an element in a finite group $G$, and let $k$ be an integer coprime to $|g|$. Prove that $g$ is a commutator in $G$ if and only if $g^k$ is a commutator.
It is obvious that if $g$ is a commutator, i.e., $g\in G'$ then $g^k\in G'$ since $G'$ is a subgroup of $G$. I dont know how to proceed the converse. Do you have any hint?
Thanks in advance.