To solve this equation, we first need to simplify the expression on the left side by applying the laws of exponents.

Recall that when you divide two numbers with the same base, you subtract the exponents.

So, (1/3)^-2x+1 = (1/3)^(1-2x) = (1/3)^(1-2x) = 3^(2x-1)

Similarly, (1/3)^4x-5 = (1/3)^(4x-5) = 3^(5-4x)

So, the equation becomes:

3^(2x-1) / 3^(5-4x) = 1/27

Now, we can simplify the left side of the equation by subtracting the exponents again:

3^(2x-1 - (5-4x)) = 3^(2x-1 - 5 + 4x) = 3^(6x-6)

Now, the equation simplifies to:

3^(6x-6) = 1/27

To solve for x, we can rewrite 1/27 as a power of 3:

3^(-3) = 3^(6x-6)

Now we can set the exponents equal to each other:

-3 = 6x-6

Solve for x:

6x = 3

x = 3/6

x = 1/2

So, the solution to the equation is x = 1/2.