\[\frac{18^{4}}{12^{5}} = \frac{2^{4} \cdot 9^{4}}{2^{5} \cdot 6^{5}} = \frac{9^{4}}{2 \cdot 6^{5}} =\]
\[= \frac{3^{4} \cdot 3^{4}}{2 \cdot 2^{5} \cdot 3^{5}} = \frac{3^{4}}{2^{6} \cdot 3} = \frac{3^{3}}{2^{6}} = \frac{27}{64}\]