To solve this equation, we can start by simplifying both sides of the equation.

First, let's simplify the right side of the equation: (1/27)^4

(1/27)^4 = 1/27 * 1/27 * 1/27 * 1/27
= 1/531441

Now, let's simplify the left side of the equation: (1/81)^(x+2)

(1/81)^(x+2) = (1/81) * (1/81) * ... * (1/81) (x+2 times)
= 1/81^(x+2)
= 1/81^(x) * 1/81^2
= (1/81^x) * (1/6561)

Now, we can set the two sides of the equation equal to each other:

(1/81^x) * (1/6561) = 1/531441

To solve for x, we can multiply both sides of the equation by 6561:

(1/81^x) = 1/531441 * 6561
= 1/531441 * 6561/1
= 6561/531441

Now, we can take the reciprocal of both sides of the equation:

81^x = 531441/6561
81^x = 81

Since both sides of the equation have the same base (81), we can equate the exponents:

x = 1

Therefore, the solution to the equation is x = 1.