(1/3)^3x-9=(1/27)^4x+1

(1/3)^(3x - 9) = (1/27)^(4x + 1)
(1/3)^(3x - 9) = ((1/3)^3)^(4x + 1)
3x - 9 = 3(4x + 1)
3x - 9 = 12x + 3
12x - 3x = -9 - 3
9x = -12
x = -12/9
x = -1 3/9
x = -1 1/3