Question

If the simplified value of $[{(-\frac{2}{3})}^3\times (-\frac{2}{3})]÷{(-\frac{2}{3})}^2$ is $\frac{p}{q}$, where $p$ and $q$ are co-prime, then $q-p$ is:

Answer 1

$[{(-\frac{2}{3})}^3\times (-\frac{2}{3})]÷{(-\frac{2}{3})}^2$
$={(-\frac{2}{3})}^{3+1}÷{(-\frac{2}{3})}^2$
$={(-\frac{2}{3})}^4÷{(-\frac{2}{3})}^2$
$={(-\frac{2}{3})}^{4-2}$
$={(-\frac{2}{3})}^2$
$=\frac{4}{9}$

Hence, $p=4$ and $q=9$

$\therefore q-p=5$