Let G be an abelian group and let n be any positive integer. Show that the function c:G--->G defined by c(x)=x^n is a homomorphism.

I started out by thinking of the definition of a homomorphism. We have a homomorphism if c(ab)=c(a)c(b).

So c(a)c(b)

a^nb^n

since G is abelian group, a^nb^n=(ab)^n=c(ab)?