Question

Evaluate:-
$3^3\times \left(243\right){}^{-\frac{2}{3}}\times 9^{-\frac{1}{3}}$

Answer 1

Consider the given expression.

$\Rightarrow 3^3\times {\left(243\right)}^{\frac{-2}{3}}\times {\left(9\right)}^{\frac{-1}{3}}$

$\Rightarrow 3^3\times \frac{1}{{\left(3^5\right)}^{\frac{2}{3}}}\times \frac{1}{{\left(3^2\right)}^{\frac{1}{3}}}$

$\Rightarrow 3^{(3-\frac{10}{3}-\frac{2}{3})}$

$\Rightarrow 3^{-1}$

$\Rightarrow \frac{1}{3}$

Hence, this is the required value.