Question

If (9^n×3^2×(3^-n/2)-(27)^n)/(3^m×2^3)=1/27, Prove that m-n=1.

Answer 1

I suspect typos
The numerator includes a √3
the denominator is 8*3^m, which includes a power of 2

There is no way the result can be 1/27

If n=1,
(9^n×3^2×(3^-n/2)-(27)^n)
= (9^1×3^2×(3^-1/2)-(27)^1)
= (9*9/√3 - 27)
= 27(√3-1)

see where you messed up

Answer 2

The question is to prove m-n=1.

I myself feel there is typo in the denominator it should 3^3m and not 3^m rest everything is okay. I tried solving i got as m-3n=3.