Root is Commutative

Theorem
Let $x \in \R_{> 0}$ be a (strictly) positive real number.

Let $a$ and $b$ be nonzero integers.

Then:
 * $\sqrt [a] {\sqrt [b] x} = \sqrt [b] {\sqrt [a] x}$

Proof
Let $y = \sqrt [a] {\sqrt [b] x}$.

Then