Try to plot x^(2/3).. what happen for x<0 ?

[rkf]

I assume the Prime does simpy follow the basic rules of Mathematics:

In the first expression, we start with squaring x, which yields for all reals a positive result - thus the cubic root is defined everywhere.

In the second expression, the cubic root is calculated first - but for reals is only defined for x >= 0. Thus the plot is left for x < 0.