Absolute Value of Even Power
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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.
$\blacksquare$