Confusion regarding exponent algebra problem

Question

How would I evaluate something like $\big((-x)^{2}\big)^{\frac{1}{2}}$?

Normally I would do it like this:

$=\big((-x)^{2}\big)^{\frac{1}{2}}$

$=\big(x^{2}\big)^{\frac{1}{2}}$

$=\big(x\big)^{\frac{2}{2}}$

$=(x)^{1}$

$=x$

But is it just as valid to do it in the following way?

$=\big((-x)^{2}\big)^{\frac{1}{2}}$

$=\big(-x\big)^{\frac{2}{2}}$

$=\big(-x\big)^{1}$

$=-x$

Answer 1

You do it like this

$$\big((-x)^{2}\big)^{\frac{1}{2}} = (x^2)^{1/2} =: |x|$$