Even Power of Negative Real Number

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

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

Then:
 * $\left({-x}\right)^n = x^n$

Proof
From Real Numbers form Totally Ordered Field, $\R$ is a field.

By definition, $\R$ is therefore a ring.

The result follows from Power of Ring Negative.