Given the order of $x=36$ in a group, how do I compute the order of $x^{-8},x^{27} $.
Also, a similar question, for $x, y \in G$, if order of $x=2$ and order of $y=3$, what can we say about order of $xy$?
The only facts I am aware of are order of $xy$=$yx$ and for any $x,y\in G$ order of $x=y^{-1}xy$