Question

Evaluate: $\frac{\sqrt{2}}{\sqrt[3]{32}}$

• A. $2^{-\frac{1}{6}}$
• B. $2^{-6}$
• C. $2^{\frac{1}{6}}$
• D. $2^6$

Answer 1

The correct option is C $2^{\frac{1}{6}}$

$\frac{\sqrt{2}}{\sqrt[3]{32}}=\frac{2^{\frac{1}{2}}}{2^{\frac{1}{3}}}=2^{\frac{1}{2}}\times 2^{\frac{-1}{3}}=2^{\frac{1}{2}-\frac{1}{3}}=2^{\frac{1}{6}}$......(Law of indices)
Hence, option $C$ is the correct answer.