\(a\text{) }4+375.\left(\dfrac{9}{16}:\dfrac{125}{64}:\dfrac{-27}{8}\right)\\ =4-375.\left(\dfrac{9}{16}\cdot\dfrac{64}{125}\cdot\dfrac{8}{27}\right)\\ =4-375.\dfrac{32}{375}\\ =4-32=-28\\ b\text{) }\dfrac{2}{3}-4.\left(\dfrac{1}{2}+\dfrac{3}{4}\right)\\ =\dfrac{2}{3}-4\cdot\dfrac{1}{2}-4\cdot\dfrac{3}{4}\\ =\dfrac{2}{3}-2-3\\ =\dfrac{2}{3}-5=-\dfrac{13}{3}\)
\(c\text{) }\left(\dfrac{12}{35}-\dfrac{6}{7}+\dfrac{18}{14}\right):\dfrac{6}{-7}-\dfrac{-2}{5}\\ =\left(\dfrac{12}{35}-\dfrac{6}{7}+\dfrac{9}{7}\right)\cdot\dfrac{-7}{6}+\dfrac{2}{5}\\ =\dfrac{12}{35}\cdot\dfrac{-7}{6}-\dfrac{6}{7}\cdot\dfrac{-7}{6}+\dfrac{9}{7}\cdot\dfrac{-7}{6}+\dfrac{2}{5}\\ =-\dfrac{2}{5}+1-\dfrac{3}{2}+\dfrac{2}{5}\\ =1-\dfrac{3}{2}=-\dfrac{1}{2}\\ d\text{) }\left[\dfrac{-54}{64}-\left(\dfrac{1}{9}:\dfrac{8}{27}\right):\dfrac{-1}{3}\right]:\dfrac{-81}{128}\\ =\left[-\dfrac{27}{32}-\left(\dfrac{1}{9}\cdot\dfrac{27}{8}\right)\cdot\left(-3\right)\right]\cdot\dfrac{-128}{81}\\ =\left(-\dfrac{27}{32}-\dfrac{9}{8}\right)\cdot\dfrac{-128}{81}\\ =-\dfrac{63}{32}\cdot\dfrac{-128}{81}=\dfrac{28}{9}\)
#$\mathtt{Toru}$
