Domain of function $x^{1/2}$

Question

What different of 2 function: $\sqrt{x}$ and $x^{1/2}$? Why domain of $\sqrt{x}$ is $x \ge 0$ but domain of $x^{1/2}$ is $x>0$?

Answer 1

The two functions are actually the same. Maybe you're talking about $x^{-1/2}$, whose domain is $x>0$, instead of $x^{1/2}$.