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?
Right, there is no need, since the following holds:
$|x|^{2n} = |x^{2n}| = x^{2n}$
for each integer $n\geq 0$.