Let $K$ be any field and $s$ an indeterminate. Then $K(s)$ is a field extension of $K (s^n )$. Prove that $[K (s):K (s^n )]=n$. Hence show that the minimum polynomial of $s$ over $K(s^n)$ is $t^n ā s^n$.
[Hint: first show that $s$ satisfies a poly of degree $n$ over $K(s^n)$; this gives $\leq$. Then show that $\{1, s, \ldots, s^{nā1}\}$ is Linearly Independent over $K(s^n)$; this gives $\geq$.]
I would really like some help with this please!