Q:

Domain of $y=x^2\ (2 - x)^{2/3}$ and $y=x^2\ \sqrt[3]{(2 - x)^{2}}$.

I have some problems with Domain of the following real function:
$$y=x^2\ (2 - x)^{2/3}$$
Since $t^{2/3}=\sqrt[3]{t^2}$, we can rewrite function as
$$y=x^2\ \sqrt[3]{(2 - x)^{2}}$$
thus Domain is $D=\mathbb R$. But, by Wolfram:
$$D=\{x \in\mathbb R : x\leq 2\}$$
Why? Maybe is $t^{2/3}=\sqrt[3]{t^2}$ not always possible?
Thanks in advance.

A:

For the set of complex numbers, the answer from Wolfram alpha is correct
But for the set of real numbers, your answer is correct.

