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

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Hint: - Use BODMAS rule.
$\left[ {{{\left( {\dfrac{{ - 2}}{3}} \right)}^3} + \left( {\dfrac{4}{9}} \right)} \right] \div {\left( {\dfrac{5}{3}} \right)^3}$
Simplify this equation using BODMAS rule
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}} \\
$
Now above equation is written as
$\left[ {\dfrac{4}{{27}}} \right] \div \dfrac{{125}}{{27}} = \dfrac{{\dfrac{4}{{27}}}}{{\dfrac{{125}}{{27}}}} = \dfrac{4}{{27}} \times \dfrac{{27}}{{125}} = \dfrac{4}{{125}}$
Note: - In such types of questions the key concept is that simplify this equation using BODMAS rule which is a bracket of division, multiplication, addition and subtraction, then after simplification we will get the required answer.

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