Question

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

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

Answer 1

The correct option is D

$\frac{64}{729}$

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

$=(\frac{2}{3}{)}^2÷1(\because a^0=1)$

$\therefore \frac{p}{q}=\frac{4}{9}$ ($\because (\frac{a}{b}{)}^m=\frac{a^m}{b^m}$)

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

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