Evaluate:

$\sqrt[3]{-216}$

By prime factorisation:

$216=2 \times 2 \times 2 \times 3 \times 3 \times 3$

$=(2 \times 2 \times 2) \times(3 \times 3 \times 3)$

$\sqrt[3]{-216}=-(2 \times 3)=-6$

$\therefore \sqrt[3]{-216}=-(\sqrt[3]{216})=-6$