\(a.\dfrac{11\cdot3^{22}\cdot3^7-9^{15}}{\left(2\cdot3^{14}\right)^2}\\ =\dfrac{11\cdot3^{29}-\left(3^2\right)^{15}}{2^2\cdot3^{28}}\\ =\dfrac{11\cdot3^{29}-3^{30}}{4\cdot3^{28}}\\ =\dfrac{3^{28}\cdot\left(11\cdot3-3^2\right)}{4\cdot3^{28}}\\ =\dfrac{33-9}{4}\\ =\dfrac{24}{4}=6\\ b.\dfrac{2^{10}\cdot3^{10}-2^{10}\cdot3^9}{2^9\cdot3^{10}}\\ =\dfrac{2^{10}\cdot3^9\cdot\left(3-1\right)}{2^9\cdot3^{10}}\\ =\dfrac{2\cdot2}{3}\\ =\dfrac{4}{3}\\ c.\dfrac{4^5\cdot9^4-2\cdot6^9}{2^{10}\cdot3^8+6^8\cdot20}\\ =\dfrac{\left(2^2\right)^5\cdot\left(3^2\right)^4-2\cdot3^9\cdot2^9}{2^{10}\cdot3^8+3^8\cdot2^8\cdot2^2\cdot5}\\ =\dfrac{2^{10}\cdot3^8-2^{10}\cdot3^9}{2^{10}\cdot3^8\cdot\left(1+5\right)}\\ =\dfrac{2^{10}\cdot3^8\cdot\left(1-3\right)}{1+5}\\ =\dfrac{-2}{6}\\ =-\dfrac{1}{3}\)
