Real Number to Negative Power

Theorem

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

Positive Integer

Let $n \in \Z_{\ge 0}$ be a positive integer.

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

Then:

$r^{-n} = \dfrac 1 {r^n}$

Integer

Let $n \in \Z$ be an integer.

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

Then:

$r^{-n} = \dfrac 1 {r^n}$

Rational Number

Real Number to Negative Power/Rational Number