81^(n+1) / 9^(2n-1)

Step 1: Rewrite 81 as 9^2: (9^2)^(n+1) / 9^(2n-1).

Step 2: Simplify the numerator: 9^(2n+2) / 9^(2n-1).

Step 3: Subtract the exponents: 9^((2n+2) - (2n-1)) = 9^(2n+2-2n+1) = 9^3 = 729.