Determine the order of $\displaystyle a^m$ where $\displaystyle a$ is an element of order $\displaystyle n$ in a group G

I don't really know what they book is looking for here. It seems to me this will break down into a bunch of cases depending on what $\displaystyle m$ and $\displaystyle n$ are, but maybe I'm wrong.

$\displaystyle a^n=1$ (the identity)

and yeah that's pretty much all I got so far