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> Show that $(xy)^n=x^ny^n$ if $xy=yx$. 
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I assume I will need 3 different cases: $n < 0$, $n=0$, and $n > 0$.

For the $n > 0$ case, can I use induction? For the base case I'll show that if $n=$1 then $(xy)^1=x^1y^1$ which will give us xy=xy so the base case is satisfied. Then I'll assume that the statement is true for n+1. Is that on the right track? 

For $n=0$, is it just trivial? that $(xy)^0=x^0y^0$ and when talking about groups $x^0=1$ so we will have $1=$1 which is true. 

For $n < 0$, I was advised to use $(xy)^n=((xy)^{-1})^{-n}$. I'm not exactly sure how to go about this step. 

I don't think I completely understand the part where this only works when $xy=yx$. 

Any suggestions or help would be great! Thanks!