若9^n·27^n-1/3^3n+1=81,求n^-2的值.答的好加奖金.

若9^n·27^n-1/3^3n+1=81,求n^-2的值.答的好加奖金.

9^n×27^(n-1)÷3^(3n+1)=81
(3²)^n×(3³)^(n-1)÷3^(3n+1)=3^4
(3^2n)×[3^3(n-1)]÷3^(3n+1)=3^4
(3^2n)×[3^(3n-3)]÷[3^(3n+1)]=3^4
3^[2n+(3n-3)-(3n+1)]=3^4
3^(2n+3n-3-3n-1)=3^4
3^(2n-4)=3^4
2n-4=4
n=4
n^-2=4^-2
=1/4²
=1/16