Find a non-abelian group $G$ and a positive integer m such that for all $g,h \in G$, $(gh)^m = g^mh^m$and $(gh)^{m+1} = g^{m+1}h^{m+1}.$ Find a non-abelian group $G$ and a positive integer m such that for all $g,h \in G$, $$(gh)^m = g^mh^m$$ and $$(gh)^{m+1} = g^{m+1}h^{m+1}.$$ 
I can't find an example.

Hint: such $m$ exists for any finite group. Can you tell what $g^{|G|}$ is? And so what about $g^{|G|+1}$?
