Question

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

• A. $\frac{28}{54}$
• B. $\frac{54}{28}$
• C. $\frac{729}{64}$
• D. $\frac{64}{729}$

Answer 1

The correct option is C $\frac{729}{64}$

$\frac{p}{q}={\left(\frac{2}{3}\right)}^2÷{\left(\frac{6}{7}\right)}^0$
$={\left(\frac{2}{3}\right)}^2÷1[a^0=1]$
$\frac{p}{q}=\frac{4}{9}$
$\frac{q}{p}=\frac{9}{4}\Rightarrow {\left(\frac{q}{p}\right)}^3={\left(\frac{9}{4}\right)}^3=\frac{729}{64}$