Evaluate:

$\sqrt[3]{\frac{125}{216}}$

By prime factorisation:

                 

$\sqrt[3]{\frac{125}{216}}=\frac{\sqrt[3]{5 \times 5 \times 5}}{\sqrt[3]{(2 \times 2 \times 2) \times(3 \times 3 \times 3)}}=\frac{\sqrt[3]{5 \times 5 \times 5}}{\sqrt[3]{(6 \times 6 \times 6)}}=\frac{5}{6}$

$\therefore \sqrt[3]{\frac{125}{216}}=\frac{5}{6}$