Evaluate:

$\sqrt[3]{\frac{27}{64}}$

By prime factorisation:

$\sqrt[3]{\frac{27}{64}}=\frac{\sqrt[3]{27}}{\sqrt[3]{64}}=\frac{\sqrt[3]{(3 \times 3 \times 3)}}{\sqrt[3]{(2 \times 2 \times 2) \times(2 \times 2 \times 2)}}=\frac{\sqrt[3]{(3 \times 3 \times 3)}}{\sqrt[3]{(4 \times 4 \times 4)}}=\frac{3}{4}$

$\therefore \sqrt[3]{\frac{27}{64}}=\frac{3}{4}$