To solve the equation 36^(-3x + 3) = (1/216)^(x + 1), we can simplify both sides of the equation using the fact that 36 can be written as (6^2) and 216 can be written as (6^3):
(6^2)^(-3x + 3) = (1 / (6^3))^(x + 1)
Now we can simplify further:
6^(-6x + 6) = 6^(-3(x + 1))
In order for the bases to be equal, the exponents must be equal. Therefore:
-6x + 6 = -3(x + 1)
Now we can solve this equation for x:
-6x + 6 = -3x - 3
To isolate the variable x, we can simplify and solve:
-6x + 3x = -3 - 6
-3x = -9
Dividing both sides by -3:
x = -9 / -3
x = 3
Therefore, the solution to the equation is x = 3.