let $a\sim b$ iff for some integer $k$, $a^k = b^k$ Let $G$ be a group, 
 Let $a\sim b$ iff  for some integer $m$, $a^m = b^m$.
I am having a problem trying to figure out how to prove that the transitive property. I know that you start off by Assuming $a\sim b$ and $b\sim c$, such that $a^m = b^m$ and $b^n = c^n$ for some $m$, $n$ that exist in the integers. I am stuck and not sure where to go from here. I just need a nudge in the right direction. 

Note that $a^{mn}=b^{mn}$ and $b^{nm}=c^{nm}$.
Remark: The relation is uninteresting if we allow exponents to be $0$.
