Absolute Value of Even Power

Theorem

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

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

Then:

$\left\vert{x^{2 n} }\right\vert = x^{2 n}$

Proof

From Even Power is Non-Negative:

$x^{2 n} \ge 0$

The result follows from the definition of absolute value.

$\blacksquare$