Question

Simplify ${\left[{\left(\frac{2}{3}\right)}^2\right]}^3\times {\left(\frac{1}{3}\right)}^{-2}\times 3^{-1}\times \frac{1}{6}$

Answer 1

$=\left[\right(\frac{2}{3}{)}^2{]}^3\times [\frac{1}{3}{]}^{-2}\times 3^{-1}\times \frac{1}{6}$

$=(\frac{2}{3}{)}^6\times (3{)}^2\times \frac{1}{3}\times \frac{1}{6}$

$=\frac{2^6}{3^6}\times \frac{1}{2}$

$=\frac{2^5}{3^6}$

$=\frac{32}{729}$