A cube root gets you a number that when you multiply by itself three times, you get the number that was being cube rooted.
For example, 2 * 2 * 2 = 8, so ∛(8) = 2. You multiply 2 three times and then you get 8, so cube root of 8 is 2.
Note this works for negative numbers. (-2) * (-2) * (-2) = 4 * (-2) = -8, so it is that we get
∛(-8) = -2
and we get ∛27 = 3 because 3 *3*3 = 27.
We also apply ∛(x/y) = ∛x / ∛y again to get
∛(-8/27) = ∛(-8)/∛(27) = -2/3