a lot of the time typing doesn't always work as smoothly as simply writing the expression down.
so it seems we have a fraction with 1 in the top and this ugliness underneath: (x^2)^(-1/3)
we can look at it this way [1/x^2]^(-1/3)...in other words you can put the exponent on the 1 also and it wouldn't change anything, except maybe make it look nicer.
now any expression with a negative exponent can be reciprocated (fancy word for flipped upside down) and the exponent then becomes positive. this leads us to...
[x^2/1]^(1/3) which is reall just [x^2]^(1/3)
now if u have (x^a)^b all you do is multiply the exponents and get x^(ab)
so that's what we do: [x^2]^(1/3) = x^(2/3)