Rational Power of Product of Real Numbers

Theorem
Let $r, s \in \R_{> 0}$ be (strictly) positive real numbers. Let $x \in \Q$ be a rational number.

Let $r^x$ be defined as $r$ to the power of $x$.

Then:
 * $\paren {r s}^x = r^x s^x$

Proof
Let $x = \dfrac p q$ where $p, q \in \Z$ and $q > 0$.

We have: