$\mathbb{F} \subset \mathbb{E}$ is a cyclotomic extension, if $\mathbb{E}$ is the splitting field of $x^n-1$ over $\mathbb{F}$.
We were directly told that $\mathbb{E} \mid \mathbb{F}$ is a Galois extension. $\mathbb{E}$ being normal is given, it is a splitting field of $x^n-1$. But what about separability? I do not remember being given a criteria to see separability of an extension, so how can I see that this is a separable extension?. I vaguely remembered looking for possible criterions for a separable extension but it wasn't exactly helpful (for my level).
Edit: as Ravi Fernando suggested, we are under the assumption that $\text{char}(\mathbb{F})=p$ prime, and $p \nmid n$.