a: \(=\dfrac{-8}{5}\cdot\dfrac{-1}{2}+\dfrac{-8}{5}\cdot\dfrac{-1}{3}\)
\(=\dfrac{-8}{5}\left(-\dfrac{1}{2}-\dfrac{1}{3}\right)=\dfrac{-8}{5}\cdot\dfrac{-5}{6}=\dfrac{8}{6}=\dfrac{4}{3}\)
b: \(=5:\dfrac{5}{3}+7:\dfrac{5}{3}\)
\(=5\cdot\dfrac{3}{5}+7\cdot\dfrac{3}{5}=\dfrac{3}{5}\cdot12=\dfrac{36}{5}\)
c: \(=13+\dfrac{3}{4}-9-\dfrac{5}{6}+7+\dfrac{1}{2}-3-\dfrac{2}{3}\)
\(=8+\dfrac{9}{12}-\dfrac{10}{12}+\dfrac{6}{12}-\dfrac{8}{12}\)
\(=8-\dfrac{3}{12}=8-\dfrac{1}{4}=\dfrac{31}{4}\)
d: \(=\dfrac{2^{10}\cdot3^{31}+2^{40}\cdot3^6}{2^{11}\cdot3^{31}+2^{41}\cdot3^6}\)
\(=\dfrac{2^{10}\cdot3^6\left(3^{25}+2^{30}\right)}{2^{11}\cdot3^6\left(3^{25}+2^{30}\right)}=\dfrac{1}{2}\)
e: \(=\left(3+\dfrac{3}{7}\right)\cdot\left(4+\dfrac{1}{5}+2+\dfrac{4}{5}\right)+\dfrac{4}{7}\left(4.2+2.8\right)\)
\(=\dfrac{24}{7}\cdot7+\dfrac{4}{7}\cdot7=7\cdot\dfrac{28}{7}=28\)
f: \(=\dfrac{1}{3}\cdot\dfrac{1}{4}-\dfrac{1}{3}\cdot\dfrac{1}{2}-\dfrac{1}{2}\cdot\dfrac{1}{4}+\dfrac{1}{2}\cdot\dfrac{1}{3}-\dfrac{5}{6}\cdot\dfrac{1}{4}\)
\(=\dfrac{1}{3}\cdot\dfrac{1}{4}-\dfrac{1}{2}\cdot\dfrac{1}{4}-\dfrac{5}{6}\cdot\dfrac{1}{4}\)
\(=\dfrac{1}{4}\cdot\left(-1\right)=-\dfrac{1}{4}\)