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The Value of { 8 − 4 / 3 ÷ 2 − 2 } 1 / 2 is - Mathematics

MCQ

The value of \[\left\{ 8^{- 4/3} \div 2^{- 2} \right\}^{1/2}\] is

Options

  • \[\frac{1}{2}\]

  • 2

  • \[\frac{1}{4}\]

  • 4

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Solution

Find the value of `{8^ (- 4/3)÷ 2^-2}^(1/2)`

   `{8^ (- 4/3)÷ 2^-2}^(1/2) = {2^(3x-4/3)÷2^-2 }^(1/2)`

                       `= {2^(3x(-4)/3)÷2^-2 }^(1/2)`

                       `= {2^-4 ÷2^-2 }^(1/2)`

`{8^ (- 4/3)÷ 2^-2}^(1/2) = {2^(-4xx1/2)÷ 2^(-2xx1/2)}`

`= {2^(-4xx1/2)÷ 2^(-2xx1/2)}`

` = {2^2 ÷ 2^-1}`

  ` = {(1/2^2)/(1/2)}`

`{8^ (- 4/3)÷ 2^-2}^(1/2) = {1/(2xx2) xx 2/1}`

                                 =`{1/(2xx2) xx 2/1}`

                                     = `1/2`

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 2 Exponents of Real Numbers
Q 16 | Page 31
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