Sign of Odd Power/Corollary

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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.

$\blacksquare$