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Number systems — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsNumber systems1 Mark
MCQ
The value of $\Big\{8^{-\frac{4}{3}}\div2^{-2}\Big\}^{\frac{1}{2}}$ is:
  • A
    $\frac{1}{2}$
  • B
    $2$
  • C
    $\frac{1}{4}$
  • D
    $4$
✓

Answer

  1. $\frac{1}{2}$
    Solution:
    Find the value of $\Big\{8^{-\frac{4}{3}}\div2^{-2}\Big\}^{\frac{1}{2}}$
    $\Big\{8^{-\frac{4}{3}}\div2^{-2}\Big\}^{\frac{1}{2}}=\Big\{2^{3\times\frac{-4}{3}}\div2^{-2}\Big\}^{\frac{1}{2}}$
    $\big\{2^{-4}\div2^{-2}\big\}^{\frac{1}{2}}$
    $\Big\{8^{-\frac{4}{3}}\div2^{-2}\Big\}^{\frac{1}{2}}=\Big\{2^{-4\times\frac{1}{2}}\div2^{-2\times\frac{1}{2}}\Big\}$
    $=\Big\{2^{-2}\div2^{-1}\Big\}$
    $=\Bigg\{\frac{\frac{1}{2^2}}{\frac{1}{2}}\Bigg\}$
    $\Big\{8^{-\frac{4}{3}}\div2^{-2}\Big\}^{\frac{1}{2}}=\Big\{\frac{1}{2\times2}\times\frac{2}{1}\Big\}$
    $=\frac{1}{2}$
    Hence the correct choice is a.

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