Evaluate

$\sqrt[3]{\frac{-64}{125}}$

By prime factorisation method:

$\sqrt[3]{\frac{-64}{125}}=\frac{\sqrt[3]{-64}}{\sqrt[3]{125}}=\frac{\sqrt[3]{(-4) \times(-4) \times(-4)}}{\sqrt[3]{5 \times 5 \times 5}}=\frac{\sqrt[3]{(-4)^{3}}}{\sqrt[3]{(5)^{3}}}$

$\sqrt[3]{\frac{-64}{125}}=\frac{-4}{5}$

$\therefore \sqrt[3]{\frac{-64}{125}}=\frac{-4}{5}$