Question

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

A
18
B
181
C
281
D
181

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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