Let E/F an algebraic field extension and let p=CharF>0 .

Let a be an elemnt in E.

prove that there exists i>=0 such as a^p^i is separable.

i thought to use to fact that if F is a field with Char p >0, and

f(x)=g(x^p) for some g over F, then f(x) (which its root is a) isn't separable..

but i'm not quite sure how to use it...

Thanks in advance