Question

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

• A. $\frac{1}{8}$
• B. $\frac{1}{81}$
• C. $\frac{2}{81}$
• D. $-\frac{1}{81}$

Answer 1

Answer: (B)

$\frac{1}{81}$

${\left\{{\sqrt[4]{4\left(\frac{1}{x}\right)}}^{-12}\right\}}^{\frac{-2}{3}},x=9$

$\Rightarrow {\left\{{\sqrt[4]{4x^{-1}}}^{-12}\right\}}^{\frac{-2}{3}}$

$\Rightarrow {\left\{\right(x^{-1}{)}^{\frac{-12}{4}}\}}^{-2/3}$

$\Rightarrow {\left\{\right(x^{-1}{)}^{-3}\}}^{-2/3}$

$\Rightarrow (x^{-1}{)}^2$

$\Rightarrow x^{-2}$

$\Rightarrow 9^{-2}$

$\Rightarrow \frac{1}{9^2}\Rightarrow \frac{1}{81}$