Question

Find the value of $m$
${\left(\frac{2}{9}\right)}^3\times {\left(\frac{2}{9}\right)}^6={\left(\frac{2}{9}\right)}^{2m-1}$

Answer 1

${\left(\frac{2}{9}\right)}^3\times {\left(\frac{2}{9}\right)}^6={\left(\frac{2}{9}\right)}^{2m-1}$

$\Rightarrow {\left(\frac{2}{9}\right)}^{3+6}={\left(\frac{2}{9}\right)}^{2m-1}$

Since bases are same, we can equate the powers,

$\Rightarrow 9=2m-1$

$\Rightarrow 2m=10$ or $m=\frac{10}{2}=5$

$\therefore m=5$