Let G be a group, and $\displaystyle a,b\in{G}$. For any positive integer$\displaystyle n$ we define $\displaystyle a^n$ by

$\displaystyle a^n=\underbrace{aaa...a}_{\text{n factors}}$ .

Now prove by induction:

If $\displaystyle ab=ba$, then $\displaystyle (ab)^n=a^nb^n$

*edit: Please, no spoilers. Just a nudge is all I need. Thanks.