Field extension $\mathbb{F}_p(X^p,Y^p)\subset\mathbb{F}_p(X,Y)$ not a primitive extension

Question

How do I prove that $\mathbb{F}_p(X^p,Y^p)\subset\mathbb{F}_p(X,Y)$ is not a primitive extension?

And how can I give infinitely many fields $E$ such that $\mathbb{F}_p(X^p,Y^p)\subset E\subset\mathbb{F}_p(X,Y)$?

Answer 1

This happens to be written on wikipedia: prove that any element in $\mathbb{F}_p(x,y)$ has degree $p$ over $\mathbb{F}_p(x^p,y^p)$.