To simplify this expression, we can first combine like terms in the numerator and denominator:

(3x)^2 = 9x^2
x^-8 = 1/x^8
x^-12 = 1/x^12

Now we can rewrite the expression as:

(9x^2 1/x^8) / (1/x^12 4x^5)

Next, let's simplify by multiplying the numerators and denominators separately:

Numerator: 9x^2 1 = 9x^2
Denominator: 1/x^12 4x^5 = 4x^5 / x^12 = 4/x^7

So the simplified expression is:

9x^2 / 4/x^7

To simplify further, we can rewrite this as:

9x^2 * x^7 / 4
= (9x^9) / 4

Therefore, the final simplified form of the expression is: 9x^9 / 4.