Say $F$ is a field of characteristic $p$ and let $f(x) = x^p - a \in F[x]$. Show that $f$ is irreducible over $F$ or $f$ splits in $F$.
Well, my solution would be since $Char F = p$, then $(x - a^{1/p})^p = x^p - a$. Therefore, $f$ splits in $F$. Is that correct?