i am practicing to draw the graphs of some rational power functions to identify vertical tangents and cusp for instance

$$f(x)=(2-x)^{\frac{1}{5}}$$

But one of my friends said that the domain of $f(x)^x$ if $x$ is a rational number is all $x$ for which $f(x) \gt 0$.

And as he said Yes, some graphing calculators is giving according to the domain what my friend said, but some giving the domain as $\mathbb{R}$. so which domain we should consider?