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Q. \( \left\{8^{-\frac{4}{3}} \div 2^{-2}\right\}^{\frac{1}{2}} \)
(a) \( \frac{1}{2} \) (b) 2 (c) \( \frac{1}{4} \) (d) 4
✏️ Solution
\( 8 = 2^3 \)
\( 8^{-\frac{4}{3}} = (2^3)^{-\frac{4}{3}} \)
\( = 2^{-4} \)
\( = \frac{1}{16} \)
\( \frac{1}{16} \div 2^{-2} = \frac{1}{16} \div \frac{1}{4} \)
\( = \frac{1}{4} \)
\( \left(\frac{1}{4}\right)^{\frac{1}{2}} \)
\( = \frac{1}{2} \)
Correct Option: (a) \( \frac{1}{2} \)
\( \boxed{\frac{1}{2}} \)