To solve the equation (-1/3)^(x-3) = (1/3)^4, we can start by simplifying both sides of the equation.

First, let's simplify the right side of the equation:
(1/3)^4 = 1/81

Now, let's simplify the left side of the equation:
(-1/3)^(x-3) = (-1/3)^(x) * (-1/3)^(-3)
= (-1/3)^(x) * (1/(-1/3)^3)
= (-1/3)^(x) * (1/(-1/27))
= (-1/3)^(x) * (-27/1)
= -27/(-3)^(x)

Now, we can rewrite the equation as:
-27/(-3)^(x) = 1/81

To solve for x, we can cross-multiply:
-27 = (1/81) * (-3)^(x)

Next, we can simplify the right side of the equation:
-27 = (-3)^(x-4)

Since the bases are the same, we can equate the exponents:
x - 4 = -27

Finally, we can solve for x:
x = -27 + 4
x = -23

Therefore, the solution to the equation (-1/3)^(x-3) = (1/3)^4 is x = -23.