If `(9^nxx3^2xx(3^(-n/2))^(-2)-(27)^n)/(3^(3m)xx2^3)=1/(27),` Prove that `m-n=1.`

Explanation

`(9^nxx3^2xx(3^(-n/2))^(-2)-(27)^n)/(3^(3m)x2^3)=1/(27)`
`(9^n*3^2*3^n−(27)^n)/(3^m*2)^3=3^(−3)`
`(3^3n*3^2−3^3n)/(3^3m.2^3)=1/3^3`
`(3^3n(3^2−1))/(3^(3m)xx8)=1/3^3`
`(3^(3n)xx8)/(3^(3m)xx8)=1/3^3`
`1/3^(3(m−n))=1/3^(3−1)`
On comparing both the sided, we get:
`m−n=1`(Proved)