Question

if {9^n+1×(3-n/2)^-2-27^n}÷(3^m×2)^3 = 1÷729 , prove that m-n=2

Answer 1

(9n+1)x(3-n/2)-2 - 27n / (3m x 2)3 =1/729

32n+2 x 3n - 33n / 3m x 2m = 1/36

33n+2 - 33n / 33m x 23 = 1/36

33n (32 - 1) / 33m x 23 = 1/36

3n (32 - 1) / 3m x 8 = 1/36

3n x (9-1) / 3m x 8 = 1/36

3n x 8 /3m x 8 = 1/36

3n / 3m = 1/36