The correct option is D 2^16 ⇒ #160; √(√(2^2)) ⇒ #160; [(2^2)^13]^14 ⇒ #160; (2)^2×13×14 ⇒ #160; #160; ...

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√√22 equal

Question

$\sqrt[4]{\sqrt[3]{2^{2}}}$ equal

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

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2^{- 6}

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

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2^{6}

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Solution

The correct option is D $2^{\frac{1}{6}}$
$\Rightarrow$ $\sqrt[4]{\sqrt[3]{2^{2}}}$

$\Rightarrow$ $[(2^{2})^{\frac{1}{3}}]^{\frac{1}{4}}$

$\Rightarrow$ $(2)^{2 \times \frac{1}{3} \times \frac{1}{4}}$

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

$∴$ $\sqrt[4]{\sqrt[3]{2^{2}}} = 2^{\frac{1}{6}}$

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Similar questions

$\sqrt[4]{\sqrt[3]{2^{2}}}$ equals to

A.) $2^{\frac{- 1}{6}}$
B.) $2^{- 6}$
C.) $2^{\frac{1}{6}}$
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$\sqrt[4]{\sqrt[3]{2^{2}}}$ equals to

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