Question
The value of $\Big\{8^{-\frac{4}{3}}\div2^{-2}\Big\}^{\frac{1}{2}}$ is:
✓
Answer
- $\frac{1}{2}$
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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