Question

Find the reciprocal of the rational number ${\left(\frac{1}{2}\right)}^2÷{\left(\frac{2}{3}\right)}^3.$

Answer 1

Given, ${\left(\frac{1}{2}\right)}^2÷{\left(\frac{2}{3}\right)}^3=\frac{{\left(\frac{1}{2}\right)}^2}{{\left(\frac{2}{3}\right)}^3}$
$=\frac{\frac{(1{)}^2}{(2{)}^2}}{\frac{(2{)}^3}{(3{)}^3}}=\frac{\left(\frac{1}{4}\right)}{\left(\frac{8}{27}\right)}$
$=\frac{1}{4}\times \frac{27}{8}=\frac{27}{4\times 8}=\frac{27}{32}$
we know that reciprocal of a rational number is obtained by interchanging numerator and denominator.
$\therefore$ Reciprocal of given number $=\frac{32}{27}$.