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:

$\paren {-x}^n = -\paren {x^n}$

Proof

We have:

$\size {-x}^n = \size {-\paren {x^n} }$

and the result follows from Sign of Odd Power.

$\blacksquare$