\[\frac{\left( 3^{2} \right)^{4} \bullet 5^{8}}{15^{6}} = \frac{3^{8} \bullet 5^{8}}{3^{6} \bullet 5^{6}} = 3^{2} \bullet 5^{2} =\]
\[= 9 \bullet 25 = 225.\]