[tex]\displaystyle \\
(8^5 \cdot 3^9):(2^{14}\cdot 9^3) = \\ \\
=\frac{8^5 \cdot 3^9}{2^{14}\cdot 9^3} = \\ \\ \\ = \frac{\Big(2^3\Big)^5 \cdot 3^9}{2^{14}\cdot \Big(3^2\Big)^3} = \\ \\ \\
=\frac{2^{3\times5} \cdot 3^9}{2^{14}\cdot 3^{2\times 3}}
=\frac{2^{15} \cdot 3^9}{2^{14}\cdot 3^{6}} =2^{15-14}\cdot 3^{9-6}
=2^1 \cdot 3^3 = 2 \cdot 27 = \boxed{54}[/tex]
