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Does an absolute value symbol need to be included every time a radical with a variable expression has an even index?

I understand that in some cases there needs to be a absolute value symbol just in case the variable is equal to a negative number that makes the radicand negative.

However what if there was a case such as $\sqrt{2x^4}$ where $~x=-5~$ the exponent makes the radicand positive. Regardless of any real number substituted into that case there wouldn't be any need of an absolute value symbol right?

nmasanta
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Ebener
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1 Answers1

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Right, there is no need, since the following holds:

$|x|^{2n} = |x^{2n}| = x^{2n}$

for each integer $n\geq 0$.

Wuestenfux
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