Irreducibility of $ X^{p^{n}}-a$

Question

Suppose that $\text{char}(F)=p\neq\emptyset$, and let

$$f= X^{p^{n}}-a\in F[X],\, \text{for some}\, n\in\mathbb N.$$

I need to prove that

1. The irreducible factorization of $f$ in $F[X]$ has the form $f= \big(X^{p^{k}}-c\big)^{p^{n-k}}$ for some $c\in F$.

2. $f$ is irreducible in $F[X]$ iff $a\notin F^p.$

Thanks for any help.