Question

9^m/3^-2=9^4 find the value of m

Answer 1

$\frac{{9}^{m} }{ {3}^{ -2} } = {9}^{4}$

$= > {3}^{2m} \times {3}^{2} = {3}^{8}$

$= > {3}^{2m + 2} = {3}^{8}$

$=>2m + 2 = 8$

$= > 2m = 8 - 2$

$= > m = \frac{6}{2}$

$= > m = 3$

I hope it helps you.....

Answer 2

SOLUTION :

$\bf \frac{9^{m} }{3^{-2}} = 9^4 \\ \\\rightarrow \bf (3)^{2m+2} = ((3)^{2})^{4}\\\\\rightarrow \bf (3)^{2m+2} = (3)^{8}\\\\\bf now \:bases \:are\: same\: equating \:thier\: powers\\\\\rightarrow 2m+2=8\\\\\rightarrow 2m=8-2\\\\\rightarrow 2m=6\\\\\rightarrow m=\frac{6}{2}\\\\\rightarrow m =3$