How to find fraction form of nth term in geometric sequence

Question

a₁ = 12 ; r = -3/4 ; 9th term

so I got 12*(-3/4)^(9-1) = 1.201 but I cannot get it correct because it asks for the exact answer and that's a round off. Please help.

Answer 1

a1 =12, r=-3/4

an = a1 (r)^(n-1)

a9 = 12 (-3/4)^(8) = 12 (9/16)^4= 12 (81/256)^2 = 12(6561/65536)

a9 = 78732/65536 = 9841.5/8192 = 1.20135498....

exact answer is 19683/16384 = 1 and 3299/16384

19683/16384 is in fractional form and an exact solution.

Answer 2

a₉ = 12(-3/4)⁸ = 3⁹/4⁷ = 19683/16384

Answer 3

a₉ = a₁r⁸ = 12(-3/4)⁸ = 12(6561/65536) = 19683/16384