Find the value of ' $ m $ '
$3^{-2} \times 3^{2 m+1}=3^{3}$.

Given:

Given equation is $3^{-2} \times 3^{2 m+1}=3^{3}$.

To do:

We have to find the value of $m$.

Solution:

We know that,

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

Therefore,

LHS $=3^{-2} \times 3^{2 m+1}$

$=3^{-2+2m+1}$

$=3^{2m-1}$

This implies,

$3^{2m-1}=3^3$

Comparing the powers on both sides, we get,

$2m-1=3$

$2m=3+1$

$2m=4$

$m=\frac{4}{2}$

$m=2$

The value of $m$ is $2$.