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Question

The value of $$ \left\{ \sqrt[4] { \left( \dfrac{1}{x} \right) }^{-12} \right\}^{- \frac{2}{3}} , $$ when $$x=9$$ is : 


A
18
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B
181
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C
281
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D
181
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Solution

The correct option is A $$\dfrac{1}{81}$$
$$\left \{ \sqrt[4]{(\dfrac{1}{x})}^{-12} \right \}^{\frac{-2}{3}}, x=9$$
$$\Rightarrow \left \{ \sqrt[4]{x^{-1}}^{-12} \right \}^{\frac{-2}{3}}$$
$$\Rightarrow \left \{ (x^{-1})^{\frac{-12}{4}} \right \}^{-2/3}$$
$$\Rightarrow \left \{ (x^{-1})^{-3} \right \}^{-2/3}$$
$$\Rightarrow (x^{-1})^{2}$$
$$\Rightarrow x^{-2}$$
$$\Rightarrow 9^{-2}$$
$$\Rightarrow \frac{1}{9^{2}}\Rightarrow \dfrac{1}{81}$$

Mathematics

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