27^(4x-1)=9^(3x+8) Solve the equation.

27^(4x-1)=9^(3x+8)
To solve, factor the 9 and 27.
(3^3)^(4x-1)=(3^2)^(3x+8)
To simplify each side, apply the exponent rule (a^m)^n=a^(m*n) .
3^(3*(4x-1))=3^(2*(3x+8))
3^(12x-3)=3^(6x+16)
Since both sides have the same base, to solve for the value of x, set the exponent at the left equal to the exponent at the right.
12x-3=6x+16
12x-6x=3+16
6x=19
x=19/6
Therefore, the solution is  x = 19/6 .