16) \(\dfrac{4^{22}\cdot5^{40}}{10^{41}}\)
\(=\dfrac{\left(2^2\right)^{22}\cdot5^{40}}{2^{41}\cdot5^{41}}\)
\(=\dfrac{2^{44}\cdot5^{40}}{2^{41}\cdot5^{41}}\)
\(=\dfrac{2^3\cdot1}{1\cdot5}\)
\(=\dfrac{8}{5}\)
17) \(\dfrac{8^{17}\cdot15^{23}}{12^{25}\cdot25^{11}}\)
\(=\dfrac{\left(2^3\right)^{17}\cdot3^{23}\cdot5^{23}}{3^{23}\cdot4^{23}\cdot\left(5^2\right)^{11}}\)
\(=\dfrac{2^{51}\cdot3^{23}\cdot5^{23}}{3^{23}\cdot2^{46}\cdot5^{22}}\)
\(=\dfrac{2^5\cdot1\cdot5}{1\cdot1\cdot1}\)
\(=160\)
18) \(\dfrac{25^7\cdot2^{15}}{8^5\cdot5^{12}}\)
\(=\dfrac{\left(5^2\right)^7\cdot2^{15}}{\left(2^3\right)^5\cdot5^{12}}\)
\(=\dfrac{5^{14}\cdot2^{15}}{2^{15}\cdot5^{12}}\)
\(=\dfrac{5^2\cdot1}{1\cdot1}\)
\(=25\)