Question

${\left(\frac{2}{3}\right)}^3\times {\left(\frac{5}{7}\right)}^3$ is equal to

$\left(a\right){(\frac{2}{3}\times \frac{5}{7})}^9$
$\left(b\right){(\frac{2}{3}\times \frac{5}{7})}^6$
$\left(c\right){(\frac{2}{3}\times \frac{5}{7})}^3$
$\left(d\right){(\frac{2}{3}\times \frac{5}{7})}^0$

Answer 1

Given:

${\left(\frac{2}{3}\right)}^3\times {\left(\frac{5}{7}\right)}^3$

We know that, if $a$, $b$ and $m$ are rational numbers, then
$a^m\times b^m=(ab{)}^m$

$\Rightarrow {\left(\frac{2}{3}\right)}^3\times {\left(\frac{5}{7}\right)}^3={(\frac{2}{3}\times \frac{5}{7})}^3$.Hence, Option $\left(c\right)$ is correct.