-22 equals toA- 2-1-6B- 2-6C- 2 1-6D- 26

Name: EXEMP - Grade 09 - Mathematics - Number System - Q17
Uploaded: 2022-07-04T10:36:42+05:30
Description: The answer is C. √(√(2)^2) =[√(2)^2]^1/4=[∵√(a)=a^1/n] =[2^2/3]^1/4=2^2/3.1/4 = 2^1/6 nbsp; [(a^m)^n=a^mn] ...

The answer is C. √(√(2)^2) =[√(2)^2]^1/4=[∵√(a)=a^1/n] =[2^2/3]^1/4=2^2/3.1/4 = 2^1/6 nbsp; [(a^m)^n=a^mn] ...

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Byju's Answer

Standard X

Mathematics

Proportion

√√22 equals t...

Question

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

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

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Solution

The answer is C.
$\sqrt[4]{{\sqrt[3]{2}}^{2}} = [{\sqrt[3]{2}}^{2}]^{\frac{1}{4}} = [∵ \sqrt[n]{a} = a^{1 / n}]$
$= [2^{2 / 3}]^{1 / 4} = 2^{\frac{2}{3} . \frac{1}{4}} = 2^{\frac{1}{6}} [(a^{m})^{n} = a^{m n}]$

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Similar questions

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

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

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Proportion

Standard X Mathematics

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4√3√22 equals to A.) 2−16 B.) 2−6 C.) 216 D.) 26

The answer is C. 4√3√22=[3√22]14=[∵n√a=a1/n] =[22/3]1/4=223.14=216 [(am)n=amn]

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

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

The answer is C.
$\sqrt[4]{{\sqrt[3]{2}}^{2}} = [{\sqrt[3]{2}}^{2}]^{\frac{1}{4}} = [∵ \sqrt[n]{a} = a^{1 / n}]$
$= [2^{2 / 3}]^{1 / 4} = 2^{\frac{2}{3} . \frac{1}{4}} = 2^{\frac{1}{6}} [(a^{m})^{n} = a^{m n}]$