If$ \sqrt{x^2}=|x|$, then why does $\sqrt{x^6}=x^3$ and not $|x^3|$?

Question

Since $\sqrt{x^6}=\sqrt{(x^3)^2}$, wouldn't $\sqrt{(x^3)^2}=|x^3|$?

Answer 1

Of course. $$ \sqrt{((-2)^3)^2}=\sqrt{(-8)^2}=\sqrt{8^2}=8=|(-2)^3|. $$