What is (2/3)^(-1/3)?

We can split this power into two bits - the negative sign and the fraction.

Let's deal with the negative sign first and forget about the fraction.

So a negative always means '1 over', or the fancy word for this is reciprocal. This just means that we flip the top and bottom number of our fraction over. Notice that when we have a whole number, an integer, this number is just over 1. So if we had (2)^-1/3, this would become (1/2)^1/3.

In our case then, the negative sign just flips over the 2 and 3 -> (3/2)^1/3.

Next look at the fraction in the power. With this, all we need to remember is 'root' - which is the root? The bottom is the root.

In other words, we take the bottom number of our fraction in the power and root our number to the appropriate degree. Here, with 3, we take the cube-root.

The top number works like a normal power - like a^2, we just get axa.

Combining this together, we have:

(3/2)^(1/3) = cube-root(3/2)^1 = cube root (3/2).

Now this looks horrible, but I promise that it's the answer.