Root of Reciprocal is Reciprocal of Root

Theorem
Let $x \in \R_{\ge 0}$.

Let $n \in \N$.

Let $\sqrt [n] x$ denote the $n$th root of $x$.

Then:
 * $\sqrt [n] {\dfrac 1 x} = \dfrac 1 {\sqrt [n] x}$

Proof
Let $y = \sqrt [n] {\dfrac 1 x}$.

Then:

Hence the result.