For questions like "What is the 1/2th root of x would the answer be $x^2$?
My logic is that since $$ \sqrt[\cfrac{1}{2}]{x}=x^{1/{(\cfrac{1}{2}})} $$ Which simplifies to $x^2$.
So as a general rule it could be $$ \sqrt[\cfrac{1}{a}]{x}=x^{1/{(\cfrac{1}{a}})} =x^a $$
And with a different denominator $$\sqrt[\cfrac{b}{a}]{x}=x^{1/{(\cfrac{b}{a}})} =x^{\cfrac{a}{b}}$$
This corresponds to how decimal/fractional exponents denote radicals (their inverse) while fractional radicals are easier shown with exponents.
Example : (2/3rd root of 4)
$$\sqrt[\cfrac{2}{3}]{4}=4^{1/{(\cfrac{2}{3}})} =4^{\cfrac{3}{2}}= 8$$
Example (22/7th root of π) :
$$\sqrt[\cfrac{22}{7}]{π}=π^{1/{(\cfrac{22}{7}})} =π^{\cfrac{7}{22}} \approx 1.439$$
Example (1/2th root of 1/4) :
$$\sqrt[\cfrac{1}{2}]{\cfrac{1}{4}}=\cfrac{1}{4}^{1/(\cfrac{2}{1})} =\cfrac{1}{4}^{(\cfrac{2}{1})} =\cfrac{1}{4}^{2} =\cfrac{1}{16} $$