Root of Reciprocal is Reciprocal of Root

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

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

Hence the result.