If your finding the cube root of -1000 to the third power, the third power and the cube root cancel to give you -1000.
Another way to think of it:
Cube root of -1000 * -1000 * -1000
Cube root of -1,000,000,000
Or cube root of (-1000)^(1/3) is
(-1000)^(1/3)*3 = -1000^1 = -1000
