Let G and H be two groups. If f: G $\displaystyle \rightarrow$ H is a homomorphism, a $\displaystyle \in$ G and b = f(a). If ord(a) = n, ord(b) = m, then n is a multiple of m. (Let $\displaystyle e_{1}$ be the identity of G and $\displaystyle e_{2}$ be the identity of H)

I know $\displaystyle a^n$ = ?

and that $\displaystyle b^n $= ?

I have to prove from that given that n is a multiple of m.

Can I have some help with this proof? Thanks.