\(a,A=\left(3\dfrac{5}{6}-1\dfrac{1}{3}\right)\left(3\dfrac{4}{15}-2\dfrac{3}{5}\right)=\dfrac{5}{2}.\dfrac{2}{3}=\dfrac{5}{3}\)
\(b,B=\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\dfrac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\dfrac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\dfrac{2.6}{3.5}=\dfrac{4}{5}\)
\(c,C=\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{6}\right)\left(1-\dfrac{1}{10}\right)\left(1-\dfrac{1}{15}\right)...\left(1-\dfrac{1}{210}\right)\)
\(=\dfrac{2}{3}.\dfrac{5}{6}.\dfrac{9}{10}.\dfrac{14}{15}.....\dfrac{209}{210}\)
\(=\dfrac{4}{6}.\dfrac{10}{12}.\dfrac{18}{20}.\dfrac{28}{30}....\dfrac{418}{420}=\dfrac{\left(1.4\right)\left(2.5\right)\left(3.6\right)\left(4.7\right).....\left(19.22\right)}{\left(2.3\right)\left(3.4\right)\left(4.5\right)\left(5.6\right)....\left(20.21\right)}\)
\(=\dfrac{\left(1.2.3.......19\right).\left(4.5.6.7.......22\right)}{\left(2.3.4.......20\right).\left(3.4.5.6.......21\right)}=\dfrac{11}{30}\)
