a: \(\dfrac{7}{15}\cdot\left(-\dfrac{2}{3}+\dfrac{3}{7}\right)+\dfrac{7}{15}\left(-\dfrac{1}{3}-\dfrac{3}{7}\right)\)
\(=\dfrac{7}{15}\left(-\dfrac{2}{3}+\dfrac{3}{7}-\dfrac{1}{3}-\dfrac{3}{7}\right)\)
\(=\dfrac{7}{15}\cdot\left(-1\right)=-\dfrac{7}{15}\)
b: \(\dfrac{11}{18}:\left(\dfrac{5}{6}-\dfrac{7}{13}\right)-\dfrac{11}{18}:\left(-\dfrac{7}{13}+\dfrac{1}{6}\right)\)
\(=\dfrac{11}{18}:\dfrac{65-42}{78}-\dfrac{11}{18}:\dfrac{-42+13}{78}\)
\(=\dfrac{11}{18}\cdot\dfrac{78}{23}-\dfrac{11}{18}\cdot\dfrac{78}{-29}\)
\(=\dfrac{11}{18}\left(\dfrac{78}{23}+\dfrac{78}{29}\right)\)
\(=\dfrac{11}{18}\cdot\dfrac{4056}{667}=\dfrac{676}{3}\cdot\dfrac{11}{667}=\dfrac{7436}{2001}\)
c: \(\left(-\dfrac{3}{4}+\dfrac{2}{3}\right):\dfrac{5}{11}+\left(-\dfrac{1}{4}+\dfrac{1}{3}\right):\dfrac{5}{11}\)
\(=\left(-\dfrac{3}{4}+\dfrac{2}{3}\right)\cdot\dfrac{11}{5}+\left(-\dfrac{1}{4}+\dfrac{1}{3}\right)\cdot\dfrac{11}{5}\)
\(=\dfrac{11}{5}\left(-\dfrac{3}{4}+\dfrac{2}{3}+\dfrac{-1}{4}+\dfrac{1}{3}\right)\)
\(=\dfrac{11}{5}\left(-1+1\right)=0\)
d: \(3^7\cdot\dfrac{2}{5^8}\cdot\dfrac{7}{3^6}\cdot5^7\)
\(=2\cdot7\cdot\dfrac{3^7}{3^6}\cdot\dfrac{5^7}{5^8}\)
\(=14\cdot\dfrac{3}{5}=\dfrac{42}{5}\)
e: \(\dfrac{27^{10}\cdot16^{25}}{6^{30}\cdot32^{15}}=\dfrac{3^{30}\cdot2^{100}}{2^{30}\cdot3^{30}\cdot2^{75}}=\dfrac{2^{100}}{2^{105}}=\dfrac{1}{2^5}=\dfrac{1}{32}\)
f: \(\left|\dfrac{3}{5}-\dfrac{1}{10}\right|-\sqrt{\dfrac{36}{25}}+\left(\dfrac{3}{10}\right)^5:\left(\dfrac{3}{10}\right)^4\)
\(=\left|\dfrac{6}{10}-\dfrac{1}{10}\right|-\dfrac{6}{5}+\dfrac{3}{10}\)
\(=\dfrac{5}{10}-\dfrac{12}{10}+\dfrac{3}{10}=\dfrac{-4}{10}=-\dfrac{2}{5}\)
g: \(\sqrt{144}+\sqrt{49}-10\cdot\sqrt{\dfrac{4}{25}}\)
\(=12+7-10\cdot\dfrac{2}{5}\)
\(=19-4=15\)
h: \(\left|\dfrac{7}{12}-\dfrac{5}{6}\right|+\sqrt{\dfrac{49}{36}}-\left(\dfrac{7}{12}\right)^8:\left(\dfrac{49}{144}\right)^4\)
\(=\left|\dfrac{7}{12}-\dfrac{10}{12}\right|+\dfrac{7}{6}-\left(\dfrac{7}{12}\right)^8:\left(\dfrac{7}{12}\right)^8\)
\(=\dfrac{3}{12}+\dfrac{7}{6}-1\)
\(=\dfrac{1}{4}+\dfrac{1}{6}=\dfrac{5}{12}\)
