Question

# Find the value of $\left[ {{{\left( {\dfrac{{ - 2}}{3}} \right)}^3} + \left( {\dfrac{4}{9}} \right)} \right] \div {\left( {\dfrac{5}{3}} \right)^3}$

$\left[ {{{\left( {\dfrac{{ - 2}}{3}} \right)}^3} + \left( {\dfrac{4}{9}} \right)} \right] \div {\left( {\dfrac{5}{3}} \right)^3}$
As we know ${\left( { - 2} \right)^3} = - 8,{\text{ }}{\left( 3 \right)^3} = 27,{\text{ and }}{\left( 5 \right)^3} = 125$
$\Rightarrow \left[ {{{\left( {\dfrac{{ - 2}}{3}} \right)}^3} + \left( {\dfrac{4}{9}} \right)} \right] \div {\left( {\dfrac{5}{3}} \right)^3} \\ = \left[ {\dfrac{{ - 8}}{{27}} + \dfrac{4}{9}} \right] \div \dfrac{{125}}{{27}} \\$
Multiply and divide by $3{\text{ in }}\dfrac{4}{9}$
$= \left[ {\dfrac{{ - 8}}{{27}} + \left( {\dfrac{4}{9} \times \dfrac{3}{3}} \right)} \right] \div \dfrac{{125}}{{27}} \\ = \left[ {\dfrac{{ - 8}}{{27}} + \dfrac{{12}}{{27}}} \right] \div \dfrac{{125}}{{27}} \\ \Rightarrow \left[ {\dfrac{4}{{27}}} \right] \div \dfrac{{125}}{{27}} \\$
$\left[ {\dfrac{4}{{27}}} \right] \div \dfrac{{125}}{{27}} = \dfrac{{\dfrac{4}{{27}}}}{{\dfrac{{125}}{{27}}}} = \dfrac{4}{{27}} \times \dfrac{{27}}{{125}} = \dfrac{4}{{125}}$