How to compute $x^{1/y}$?
$x^{1/y}$ is the $y$th root of $x$, i.e., the element $w$ that satisfies $w^y =x$.

If $x$ generates a group of prime order $q$, it can be shown that this element $w$ is unique and equals $x^z$ where $z$ is the inverse of $y$ modulo $q$. (One way to show this is to use the fact that $x^a = x^b$ if and only if $a \equiv b \pmod q$.)