\[\frac{9^{3}{\cdot 81}^{2}}{3^{12}} = \frac{\left( 3^{2} \right)^{3} \cdot \left( 3^{4} \right)^{2}}{3^{12}} =\]
\[= \frac{3^{6} \cdot 3^{8}}{3^{12}} = \frac{3^{14}}{3^{12}} = 3² = 9\]