Simplify the expression $$\frac{4^5 \cdot 9^3}{12^6}$$

Rewrite the bases in terms of their prime factors:

1. $$\frac{(2^2)^5 \cdot (3^2)^3}{(2^2 \cdot 3)^6}$$
2. $$\frac{2^{10} \cdot 3^6}{2^{12} \cdot 3^6}$$
3. $$2^{10-12} \cdot 3^{6-6} = 2^{-2} \cdot 3^0 = \frac{1}{2^2} \cdot 1 = \frac{1}{4}$$