Question

If 0^2/3 = 0, why is 0^-2/3 undefined?

Answer 1

Because anything raised to the negative power becomes its reciprocal, here lemme show you what i mean:

2^-1 = 1/2

3^-1 = 1/3

x^-1 = 1/x

so 0 taken to a negative power is just

1/0 = ???

I don't know about you, but I never learned to divide by zero, at least not without calculus ;)

so let's rewrite your problem as:

0^-2/3 = 1/0^(2/3) = 1/0 = undefined

Answer 2

Thanks guys :)

Answer 3

0/3 = 0 is totally different with:
0^-2/3 = 1/0 * 3 = 1/0 ( undefined!)