Question

By what number should ${(-\frac{2}{3})}^3$ be divided so that the quotient maybe equal to ${\left(\frac{9}{4}\right)}^{-2}$

Answer 1

Let $x$ be the number

$\therefore$ According to question

$\Rightarrow {\left(\frac{-2}{3}\right)}^3÷x={\left(\frac{9}{4}\right)}^{-2}$

$\Rightarrow \frac{1}{x}=\frac{{\left(\frac{9}{4}\right)}^{-2}}{{\left(\frac{-2}{3}\right)}^3}$

$\Rightarrow x=\frac{{\left(\frac{-2}{3}\right)}^3}{{\left(\frac{9}{4}\right)}^{-2}}$

$\Rightarrow x=\frac{-8}{27}\times {\left(\frac{9}{4}\right)}^2$

$\Rightarrow x=\frac{-8}{27}\times \frac{81}{16}$

$\therefore x=\frac{-3}{2}$

Hence the number is $\frac{-3}{2}$