Write the correct answer in the following: [4] [3] 2^2 equals. 1. 2^ -1 6 2. 2^ -6 3. 2^ 1 6 4. 2^ 6

3. 2^ 1 6 Solution: [4] [3] 2^2 = [4] (2^2)^ 1 3 = (2^ 2 3 )^ 1 4 =2^ 2 3 1 4 =2^ 1 6 Hence, (c) is the correct answer.

Write the correct answer in the following: [4] [3] 2^2 equals. 1.…

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Question

Write the correct answer in the following:
$\sqrt[4]{\sqrt[3]{2^2}}$ equals.

$2^{-\frac{1}{6}}$
$2^{-6}$
$2^{\frac{1}{6}}$
$2^{6}$

✓

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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