Question

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

Answer 1

`m=3^(-12)`

Explanation:

we are given that

`(9m)/(3^(-2))=9^(-4)`

`(3^(2)* m)/(3^(-2))=(3^(2))^(-4)`

applying the rule of exponents

`(m^(a))^(b)=m^(ab)`

`{3^(2)* m=3^(-8) * 3^(-2)`

`m=(3^(-8) * 3^(-2))/(3^(2))`

applying the rule of exponents

`(1)/(m^a)=m^(-a)`

`m=3^(-8) * 3^(-2)* 3^(-2)`

`m=3^(-8-2-2)`

`m=3^(-12)`

`m=(1)/(3^(12))`