Question

Solve : $[{\left(\frac{-2}{3}\right)}^3+\left(\frac{4}{9}\right)]÷{\left(\frac{5}{3}\right)}^3$

Answer 1

$I=\left[\right(\frac{-2}{3}{)}^3+\frac{4}{9}]÷{\left(\frac{5}{3}\right)}^3$

$I=[{(-\frac{2}{3})}^3+{\left(\frac{2}{3}\right)}^2]6\times {\left[\frac{3}{5}\right]}^3$

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

$\to {\left(\frac{2}{3}\right)}^2\left[\frac{1}{3}\right]\times {\left(\frac{3}{5}\right)}^3$

$=2^2\times 3^{-3}\times 3^{-3}\times 5^{-3}$

$I=4\times \frac{1}{125}$

$I=\frac{4}{125}$