Exponent Combination Laws/Negative Power of Quotient

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

Let $x \in \R$ be a real number.

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

Then:
 * $\left({\dfrac a b}\right)^{-x} = \left({\dfrac b a}\right)^x$