Let $k$ be a field of characteristic $p >0$, let $K=k(x,y)$ be the rational function field over $k$ in two variables, and let $F=k(x^p,y^p)$. Show that $K \neq F(a)$ for any $a \in K$.
For $a \in K$ $a=\frac {f(x,y)}{g(x,y)}$ but how to show that this does not generate $x,y$ individualy?