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Q. Which one is NOT equal to \( (\sqrt[3]{8})^{-1/2} \) ?
(a) \( (\sqrt[3]{2})^{-1/2} \)
(b) \( 8^{-1/6} \)
(c) \( \frac{1}{(\sqrt[3]{8})^{1/2}} \)
(d) \( \frac{1}{\sqrt{2}} \)
✏️ Solution
\( \sqrt[3]{8} = 2 \)
\( (\sqrt[3]{8})^{-1/2} = 2^{-1/2} \)
\( = \frac{1}{\sqrt{2}} \)
(a) \( (\sqrt[3]{2})^{-1/2} = 2^{-1/6} \)
\( \neq 2^{-1/2} \)
(b) \( 8^{-1/6} = (2^3)^{-1/6} = 2^{-1/2} \)
(c) \( \frac{1}{(\sqrt[3]{8})^{1/2}} = 2^{-1/2} \)
(d) \( \frac{1}{\sqrt{2}} = 2^{-1/2} \)
Correct Option: (a)
\( \boxed{(\sqrt[3]{2})^{-1/2}} \)