X^2/3 can be written as

X to the power of two thirds

X^ (1/2) = √ (x)

so, following that logic

x^ (2/3) = the third root√ (x^2)

x^ (y/z) the bottom of the fraction is the power of the root. (zth root√ (x^y)) the top is the power that x is raised inside the zth root.