Help with set theory proof

I've been given a question on my problem set which I'm a bit stuck with. I'm getting the sense that the first part is easier than the second part, but I can't even seem to get the first part!

a) Let A, X, Y be sets such that $\displaystyle X\preceq A$. Show that $\displaystyle X^Y\preceq A^Y$. Therefore show that, for cardinals $\displaystyle \kappa, \lambda, \mu $, if $\displaystyle \kappa \leq \lambda$ then $\displaystyle \kappa^\mu \leq \lambda^\mu$.

b) Let A, B, X, Y be sets with $\displaystyle X\preceq A$ and $\displaystyle Y\preceq B$. Show that, apart from some exceptional cases, $\displaystyle X^Y\preceq A^B$. What are the exceptional cases?

I'd really appreciate any help you can provide! (Nod)