Question

If $\frac{p}{q}={\left(\frac{3}{2}\right)}^{-2}÷{\left(\frac{6}{7}\right)}^0$, find the value of ${\left(\frac{p}{q}\right)}^{-3}$

Answer 1

given,

$\frac{p}{q}={\left(\frac{3}{2}\right)}^{-2}÷{\left(\frac{6}{7}\right)}^0$

$\Rightarrow \frac{p}{q}={\left(\frac{1}{\frac{3}{2}}\right)}^2÷1$

$\frac{p}{q}=\frac{4}{9}$

${\left(\frac{p}{q}\right)}^{-3}$

$={\left(\frac{1}{\frac{p}{q}}\right)}^3$

$={\left(\frac{q}{p}\right)}^3$

$={\left(\frac{9}{4}\right)}^3$

$=\frac{729}{64}$