Evaluate

$\sqrt[3]{216 \times 343}$

By prime factorisation:

$\sqrt[3]{216 \times 343}=\sqrt[3]{216} \times \sqrt[3]{343}=\sqrt[3]{2 \times 2 \times 2 \times 3 \times 3 \times 3} \times \sqrt[3]{7 \times 7 \times 7}=\sqrt[3]{(2)^{3} \times(3)^{3}} \times \sqrt[3]{(7)^{3}}$

$\sqrt[3]{216 \times 343}=(2) \times(3) \times(7)=42$

$\therefore \sqrt[3]{216 \times 343}=42$