Sign of Odd Power/Corollary

Corollary to Sign of Odd Power
Let $x \in \R$ be a real number. Let $n \in \Z$ be an odd integer.

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

Proof
We have:
 * $\left\vert{-x}\right\vert^n = \left\vert-{\left({x^n}\right)}\right\vert$

and the result follows from Sign of Odd Power.