Even Power of Negative Real Number

From ProofWiki
Jump to navigation Jump to search

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.

$\blacksquare$