Question:
Evaluate: $\sqrt[3]{4096}$
Solution:
$\sqrt[3]{4096}$
By prime factorisation method:
$\sqrt[3]{4096}=\sqrt[3]{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2}=\sqrt[3]{(2)^{3} \times(2)^{3} \times(2)^{3} \times(2)^{3}}$
$\sqrt[3]{4096}=(2) \times(2) \times(2) \times(2)=16$
$\therefore \sqrt[3]{4096}=16$