Question
Write the correct answer in the following:
$\sqrt[4]{\sqrt[3]{2^2}}$ equals.
$\sqrt[4]{\sqrt[3]{2^2}}$ equals.
✓
Answer
- $2^{\frac{1}{6}}$
Solution:
$\sqrt[4]{\sqrt[3]{2^2}}=\sqrt[4]{(2^2)^{\frac{1}{3}}}=\Big(2^{\frac{2}{3}}\Big)^{\frac{1}{4}}=2^{\frac{2}{3}\times\frac{1}{4}}=2^{\frac{1}{6}}$
Hence, (c) is the correct answer.
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