Question

By what number should ${\left(\frac{-2}{3}\right)}^{-3}$ be divided so that the quotient may be ${\left(\frac{4}{27}\right)}^{-2}$

Answer 1

Let the number be $x$

$\frac{{\left(\frac{-2}{3}\right)}^{-3}}{x}={\left(\frac{4}{27}\right)}^{-2}$

$\Rightarrow \frac{{\left(\frac{-3}{2}\right)}^3}{x}={\left(\frac{27}{4}\right)}^2$

$\Rightarrow x=\frac{(\frac{-3}{2}{)}^3}{(\frac{27}{4}{)}^2}$

$\Rightarrow x=\frac{\left(\frac{-27}{8}\right)}{\left(\frac{{27}^2}{16}\right)}$

$\Rightarrow x=\frac{-2}{27}$