\(7.\dfrac{8^3\cdot8^2}{2^{10}}=\dfrac{\left(2^3\right)^3\cdot\left(2^3\right)^2}{2^{10}}\\ =\dfrac{2^9\cdot2^6}{2^{10}}\\ =\dfrac{2^{15}}{2^{10}}\\ =2^5=32\\ 8.\dfrac{16^3\cdot8^5}{4^{12}}\\ =\dfrac{\left(2^4\right)^3\cdot\left(2^3\right)^5}{\left(2^2\right)^{12}}\\ =\dfrac{2^{12}\cdot2^{15}}{2^{24}}\\ =\dfrac{2^{27}}{2^{24}}\\ =2^3=8\\ 9.\dfrac{5^4\cdot9^5}{15^3\cdot27^2}\\ =\dfrac{5^4\cdot\left(3^2\right)^5}{5^3\cdot3^3\cdot\left(3^3\right)^2}\\ =\dfrac{5^4\cdot3^{10}}{5^3\cdot3^9}\\ =5\cdot3=15\\ 10.\dfrac{10^5\cdot7^3}{14^2\cdot20^4}\\ =\dfrac{10^5\cdot7^3}{7^2\cdot2^2\cdot\left(2^2\right)^4\cdot5^4}\\ =\dfrac{2^5\cdot5^5\cdot7^3}{2^{10}\cdot5^4\cdot7^2}\\ =\dfrac{5\cdot7}{2^5}=\dfrac{35}{32}\)
