Let $T$ be a torus, $m$ a positive integer. Prove that the morphism $x \mapsto x^m$ maps onto $T$, and is separable if $(p,m)=1$.
Here, $p$ $(>0)$ is the characteristic of the base field. A dominant morphism $\phi: X \rightarrow Y$ of irreducible algebraic varieties is called separable if the field extension $K[X]/\phi^*(K[Y])$ is separable.
It seems not easy to prove the separability of the field extension.