\(a.\left(4\cdot2^5\right):\left(2^3\cdot\dfrac{1}{16}\right)\\ =\left(4\cdot2^5\right):\left(2^3\cdot\dfrac{1}{2^4}\right)\\ =2^2\cdot2^5\cdot2\\ =2^8\\ b.\dfrac{6^7\cdot2^9}{4^8\cdot9^4}\\ =\dfrac{2^7\cdot3^7\cdot2^9}{\left(2^2\right)^8\cdot\left(3^2\right)^4}\\ =\dfrac{2^{15}\cdot3^7}{2^{16}\cdot3^8}\\ =\dfrac{1}{2\cdot3}=\dfrac{1}{6}\\ c.\dfrac{6^3+3\cdot6^2+3^3}{-13}\\ =\dfrac{3^3\cdot2^3+3^3\cdot2^2+3^3}{-13}\\ =\dfrac{3^3\cdot\left(2^3+2^2+1\right)}{-13}\\ =\dfrac{3^3\cdot13}{-13}=-3^3=-27\\ d.\dfrac{8^5\cdot\left(-5\right)^8+\left(-2\right)^5\cdot10^9}{2^{16}\cdot5^7+20^8}\\ =\dfrac{\left(2^3\right)^5\cdot5^8-2^5\cdot2^9\cdot5^9}{2^{16}\cdot5^7+\left(2^2\right)^8\cdot5^8}\\ =\dfrac{2^{15}\cdot5^8-2^{14}\cdot5^9}{2^{16}\cdot5^7+2^{16}\cdot5^8}\\ =\dfrac{5^8\cdot2^{14}\cdot\left(2-5\right)}{5^7\cdot2^{16}\cdot\left(1+5\right)}\\ =\dfrac{5\cdot-3}{2^2\cdot6}\\ =\dfrac{-5}{2^3}=\dfrac{-5}{8}\)