Question

Question 70

If $\frac{p}{q}={\left(\frac{3}{2}\right)}^2÷{\left(\frac{9}{4}\right)}^0,$Find the value of ${\left(\frac{p}{q}\right)}^3.$

Answer 1

We have $,\left(\frac{p}{q}\right)={\left(\frac{3}{2}\right)}^2÷{\left(\frac{9}{4}\right)}^0\Rightarrow \frac{p}{q}={\left(\frac{3}{2}\right)}^2÷\frac{1}{1}\Rightarrow \frac{p}{q}={\left(\frac{3}{2}\right)}^2\Rightarrow \frac{p}{q}=\frac{3^2}{2^2}\Rightarrow \frac{p}{q}=\frac{9}{4}$

On taking cube both sides, we get
${\left(\frac{p}{q}\right)}^3={\left(\frac{9}{4}\right)}^3\therefore {\left(\frac{p}{q}\right)}^3=\frac{9\times 9\times 9}{4\times 4\times 4}=\frac{729}{64}$