I would have thought a Harvard candidate would be able to simplify (1/3)^(1/3) to 1/∛3 in a single step? You just take the cube root of the numerator and denominator. To my mind, that is the simplest way to write the expression. What is gained by writing it as ∛(3^2)/3? That seems more complicated than the original form. But in any case you can get from 1/∛3 to ∛(3^2)/3 in a couple of extra steps.