a: \(A=\left(-1\dfrac{1}{6}\right):\left(-12\dfrac{1}{2}+14\dfrac{1}{4}\right)-\left(-\dfrac{3}{4}\right):\left(18-16\dfrac{5}{8}\right)\)
\(=\dfrac{-7}{6}:\left(-12-\dfrac{1}{2}+14+\dfrac{1}{4}\right)+\dfrac{3}{4}:\left(18-16-\dfrac{5}{8}\right)\)
\(=\dfrac{-7}{6}:\left(2-\dfrac{1}{4}\right)+\dfrac{3}{4}:\left(2-\dfrac{5}{8}\right)\)
\(=\dfrac{-7}{6}:\dfrac{7}{4}+\dfrac{3}{4}:\dfrac{11}{8}\)
\(=\dfrac{-4}{6}+\dfrac{3}{4}\cdot\dfrac{8}{11}\)
\(=\dfrac{-2}{3}+\dfrac{6}{11}=\dfrac{-22}{33}+\dfrac{18}{33}=-\dfrac{4}{33}\)
b: \(B=\left(\dfrac{1}{4}-1\right)\left(\dfrac{1}{9}-1\right)\cdot...\cdot\left(\dfrac{1}{625}-1\right)\)
\(=\left(\dfrac{1}{2^2}-1\right)\left(\dfrac{1}{3^2}-1\right)\cdot...\cdot\left(\dfrac{1}{25^2}-1\right)\)
\(=\left(1-\dfrac{1}{2^2}\right)\left(1-\dfrac{1}{3^2}\right)\cdot...\cdot\left(1-\dfrac{1}{25^2}\right)\)
\(=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\cdot...\cdot\left(1-\dfrac{1}{25}\right)\cdot\left(1+\dfrac{1}{2}\right)\cdot\left(1+\dfrac{1}{3}\right)\cdot...\cdot\left(1+\dfrac{1}{25}\right)\)
\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{24}{25}\cdot\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{26}{25}\)
\(=\dfrac{1}{25}\cdot\dfrac{26}{2}=\dfrac{13}{25}\)
