Find the cube-roots of -512.

Prime factors of 512:

$\sqrt[3]{-512}\\[1em] = -\sqrt[3]{(2 \times 2 \times 2) \times (2 \times 2 \times 2) \times (2 \times 2 \times 2)}\\[1em] = -(2 \times 2 \times 2)\\[1em] = -8$

Hence, $\sqrt[3]{-512} = -8$