Question

Find the value of '$n$' in the following:
${\left(\frac{2}{3}\right)}^3\times {\left(\frac{2}{3}\right)}^5={\left(\frac{2}{3}\right)}^{n-2}$

Answer 1

we know,

$a^m\ast a^n=a^{m+n}$

so,

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

$={\left(\frac{2}{3}\right)}^8$

$n-2=8$

$⟹$

$n=10$