# How do you evaluate x^ { - 2} [ x ^ { 6} [ x ( x ^ { - 3} ) ^ { \frac { 1} { 3} } ] ^ { \frac { 1} { 9} } \} ^ { \frac { 2} { 3} }?

Feb 1, 2018

${x}^{2}$

#### Explanation:

Given, ${x}^{-} 2 {\left[{x}^{6} {\left\{x {\left({x}^{-} 3\right)}^{\frac{1}{3}}\right\}}^{\frac{1}{9}}\right]}^{\frac{2}{3}}$
$\Rightarrow {x}^{-} 2 {\left[{x}^{6} {\left\{{x}^{1} {\left({x}^{-} 3\right)}^{\frac{1}{3}}\right\}}^{\frac{1}{9}}\right]}^{\frac{2}{3}}$
$\Rightarrow {x}^{-} 2 {\left[{x}^{6} {\left\{{x}^{1} {x}^{-} 1\right\}}^{\frac{1}{9}}\right]}^{\frac{2}{3}}$
$\Rightarrow {x}^{-} 2 {\left[{x}^{6} {\left\{{x}^{1 - 1}\right\}}^{\frac{1}{9}}\right]}^{\frac{2}{3}}$
$\Rightarrow {x}^{-} 2 {\left[{x}^{6} {\left\{{x}^{0}\right\}}^{\frac{1}{9}}\right]}^{\frac{2}{3}}$
$\Rightarrow {x}^{-} 2 {\left[{x}^{6} {\left\{1\right\}}^{\frac{1}{9}}\right]}^{\frac{2}{3}}$
$\Rightarrow {x}^{-} 2 {\left[{x}^{6} \cdot 1\right]}^{\frac{2}{3}}$
$\Rightarrow {x}^{-} 2 {x}^{6 \cdot \frac{2}{3}}$
$\Rightarrow {x}^{-} 2 {x}^{4}$
$\Rightarrow {x}^{- 2 + 4}$
$\Rightarrow {x}^{2}$