Question

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

Answer 1

Let $a=3^3\times {\left(3^5\right)}^{\frac{-2}{3}}\times {\left(3^2\right)}^{\frac{-1}{3}}$

$=3^3\times 3^{\frac{-10}{3}}\times 3^{\frac{-2}{3}}$

$=3^{3-\frac{10}{3}-\frac{2}{3}}$

$=3^{3-\frac{12}{3}}$

$=3^{3-4}$

$=3^{-1}$

$a=\frac{1}{3}$

$\therefore 3^3\times {\left(3^5\right)}^{\frac{-2}{3}}\times {\left(3^2\right)}^{\frac{-1}{3}}=\frac{1}{3}$