a: \(=2:\left(\dfrac{3-4}{6}\right)^2+1-\dfrac{12^4}{12^2\cdot3^2}\)
\(=2:\left(\dfrac{1}{6}\right)^2+1-\dfrac{12^2}{3^2}\)
\(=2\cdot36+1-16=72+1-16=73-16=57\)
b: \(=\dfrac{1}{13}+\dfrac{-5}{8}-\dfrac{1}{13}+\dfrac{12}{17}-\dfrac{12}{17}+\dfrac{5}{18}-\dfrac{7}{5}=-\dfrac{7}{5}\)
c: \(=\dfrac{\left(0.09\cdot15\right)^5}{5^6\cdot\left(-0.9\right)^7}=\dfrac{\left(0.09\right)^5}{\left(-0.9\right)^7}\cdot\dfrac{15^5}{5^5\cdot5}\)
\(=\left(\dfrac{9}{100}\right)^5:\left(-\dfrac{9}{10}\right)^7\cdot\dfrac{3^5}{5}\)
\(=\dfrac{3^{10}}{10^{10}}:\dfrac{-3^{14}}{10^7}\cdot\dfrac{3^5}{5}\)
\(=\dfrac{3^{10}}{10^{10}}\cdot\dfrac{10^7}{-3^{14}}\cdot\dfrac{3^5}{5}\)
\(=\dfrac{-1}{3^4}\cdot3^5\cdot\dfrac{1}{10^3\cdot5}=\dfrac{-3}{10^3\cdot5}\)
