10) \(\dfrac{10^5\cdot7^3}{14^2\cdot20^4}\)
\(=\dfrac{10^5\cdot7^3}{2^2\cdot7^2\cdot10^4\cdot2^4}\)
\(=\dfrac{10^5\cdot7^3}{2^6\cdot7^2\cdot10^4}\)
\(=\dfrac{10\cdot7}{2^6\cdot1\cdot1}\)
\(=\dfrac{70}{64}\)
\(=\dfrac{35}{32}\)
11) \(\dfrac{8^3\cdot6^5}{2^{12}\cdot27^2}\)
\(=\dfrac{\left(2^3\right)^3\cdot2^5\cdot3^5}{2^{12}\cdot\left(3^3\right)^2}\)
\(=\dfrac{2^{14}\cdot3^5}{2^{12}\cdot3^6}\)
\(=\dfrac{2^2\cdot1}{1\cdot3}\)
\(=\dfrac{4}{3}\)
12) \(\dfrac{8^8\cdot3^{14}}{9^6\cdot2^{20}}\)
\(=\dfrac{\left(2^3\right)^8\cdot3^{14}}{\left(3^2\right)^6\cdot2^{20}}\)
\(=\dfrac{2^{24}\cdot3^{14}}{3^{12}\cdot2^{20}}\)
\(=\dfrac{2^4\cdot3^2}{1\cdot1}\)
\(=144\)