The value of 8-4-3- 2-21-2 is1-41-24 2

{ 8^ 4/3÷ 2^ 2}^1/2 nbsp;= [(2^3)^ 4/3÷ 2^ 2 ]^1/2= [2^3 × ( 4/3 )÷ 2^ 2 ]^1/2 nbsp; [Using (a^m)^n=a^mn]=[2^3 × 4/3÷ 2^ 2 ]^1/2= [2^ 4/2^ 2 ]^1/2= [2^2/2^4 ...

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Byju's Answer

Standard IX

Mathematics

Laws of Exponents for Real Numbers

The value of ...

Question

The value of ${8^{\frac{- 4}{3}} \div 2^{- 2}}^{\frac{1}{2}}$ is

$\frac{1}{2}$

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$\frac{1}{4}$

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Solution

Given:
${8^{\frac{- 4}{3}} \div 2^{- 2}}^{\frac{1}{2}}$
$= {[(2^{3})^{\frac{- 4}{3}} \div 2^{- 2}]}^{\frac{1}{2}}$
$= {[2^{3 \times (\frac{- 4}{3})} \div 2^{- 2}]}^{\frac{1}{2}}$ [Since, $(a^{m})^{n} = a^{m \times n}$ ]
$= {[2^{3 \times \frac{- 4}{3}} \div 2^{- 2}]}^{\frac{1}{2}}$
$= {(\frac{2^{- 4}}{2^{- 2}})}^{\frac{1}{2}}$
$= (2^{- 4 - (- 2)})^{\frac{1}{2}}$ [since, $\frac{a^{m}}{a^{n}} = a^{m - n}, a \neq 0$ ]
$= (2^{- 2})^{\frac{1}{2}}$
$= {(\frac{1}{2^{2}})}^{\frac{1}{2}}$ [Since, $a^{- m} = \frac{1}{a^{m}}$ ]
$= \frac{1}{2^{2 \times \frac{1}{2}}}$
$= \frac{1}{2}$
$∴ {8^{\frac{- 4}{3}} \div 2^{- 2}}^{\frac{1}{2}} = \frac{1}{2}$

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The value of {8−43÷2−2}12 is

Given: {8−43÷2−2}12 =[(23)−43÷2−2]12 =[23×(−43)÷2−2]12 [Since, (am)n=am×n]=[23×−43÷2−2]12=(2−42−2)12=(2−4−(−2))12 [since, aman=am−n,a≠0]=(2−2)12=(122)12 [Since, a−m=1am]=122×12=12∴{8−43÷2−2}12=12

The value of ${8^{\frac{- 4}{3}} \div 2^{- 2}}^{\frac{1}{2}}$ is