\(\frac{11\cdot3^{22}\cdot3^7-9^{15}}{\left(2\cdot3^{14}\right)^2}\)
=\(\frac{11\cdot3^{29}-3^{30}}{2^2\cdot3^{28}}\)
=\(\frac{11\cdot3^{29}-3^{29}\cdot3}{2^2\cdot3^{28}}\)
=\(\frac{3^{29}\cdot\left(11-3\right)}{2^2\cdot3^{28}}\)
=\(\frac{3^{29}\cdot2^3}{2^2\cdot3^{28}}\)
=\(\frac{3\cdot2}{1}\)
=6