Exponent Combination Laws/Power of Power/Proof 1

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

Let $x, y \in \R$ be real numbers.

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

Then:
 * $\left({a^x}\right)^y = a^{x y}$