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

$\frac{729}{64}$

$\frac{p}{q}={\left(\frac{2}{3}\right)}^2÷{\left(\frac{6}{7}\right)}^0$
$=(\frac{2}{3}{)}^2÷1)(\because a^0=1)$
$\therefore \frac{p}{q}=\frac{4}{9}$ ($\because (\frac{a}{b}{)}^m=\frac{a^m}{b^m}$)
$\Rightarrow \frac{q}{p}=\frac{9}{4}$

$\Rightarrow (\frac{q}{p}{)}^3=(\frac{9}{4}{)}^3=\frac{729}{64}$