\[\frac{3^{10} \cdot 27^{3}}{9^{9}} = \frac{3^{10} \cdot \left( 3^{3} \right)^{3}}{\left( 3^{2} \right)^{9}} =\]
\[= \frac{3^{10} \cdot 3^{9}}{3^{18}} = \frac{3^{19}}{3^{18}} = 3^{1} = 3.\]