Вычислите: а) \(\left(1\frac{17}{25}\cdot2\frac{1}{7}-2\frac{4}{7}\cdot1\frac{2}{5}\right)\cdot2\frac{7}{9}\); б) \(\frac{1}{13}\cdot\left(2\frac{3}{8}-1\frac{5}{6}\right)\cdot2\frac{2}{5}+\frac{9}{10}\); в) \(\left(4\frac{3}{4}-1\frac{2}{5}\cdot2\frac{1}{2}\right)\cdot1\frac{3}{5}\); г) \(1\frac{1}{2}\cdot\frac{2}{9}-\left(6-5\frac{3}{5}\right)^2\); д) \(\left(4\frac{1}{15}-3\frac{9}{10}\right)\cdot6\frac{6}{7}+2\); е) \(\frac{1}{3}\cdot\left(4-\left(1\frac{1}{2}\right)^4\right)\cdot\left(3-2\frac{7}{15}\right)\).

а)

\(1\frac{17}{25}=\frac{42}{25}\), \(2\frac{1}{7}=\frac{15}{7}\), \(2\frac{4}{7}=\frac{18}{7}\), \(1\frac{2}{5}=\frac{7}{5}\).

\[\left(\frac{42}{25}\cdot\frac{15}{7}-\frac{18}{7}\cdot\frac{7}{5}\right)\cdot2\frac{7}{9}=\left(\frac{18}{5}-\frac{18}{5}\right)\cdot2\frac{7}{9}=0.\]

б)

\[\frac{1}{13}\cdot\left(\frac{19}{8}-\frac{11}{6}\right)\cdot\frac{12}{5}+\frac{9}{10}=\frac{1}{13}\cdot\frac{13}{24}\cdot\frac{12}{5}+\frac{9}{10}=\frac{1}{10}+\frac{9}{10}=1.\]

в)

\[\left(\frac{19}{4}-\frac{7}{5}\cdot\frac{5}{2}\right)\cdot\frac{8}{5}=\left(\frac{19}{4}-\frac{7}{2}\right)\cdot\frac{8}{5}=\frac{5}{4}\cdot\frac{8}{5}=2.\]

г)

\[\frac{3}{2}\cdot\frac{2}{9}-\left(6-\frac{28}{5}\right)^2=\frac{1}{3}-\left(\frac{2}{5}\right)^2=\frac{1}{3}-\frac{4}{25}=\frac{13}{75}.\]

д)

\[\left(\frac{61}{15}-\frac{39}{10}\right)\cdot\frac{48}{7}+2=\left(\frac{122}{30}-\frac{117}{30}\right)\cdot\frac{48}{7}+2=\frac{1}{6}\cdot\frac{48}{7}+2=\frac{8}{7}+2=\frac{22}{7}.\]

е)

\[\frac{1}{3}\cdot\left(4-\left(\frac{3}{2}\right)^4\right)\cdot\left(3-\frac{37}{15}\right)=\frac{1}{3}\cdot\left(4-\frac{81}{16}\right)\cdot\frac{8}{15}=\frac{1}{3}\cdot\left(-\frac{17}{16}\right)\cdot\frac{8}{15}=-\frac{17}{90}.\]

Ответ: а) \(0\); б) \(1\); в) \(2\); г) \(\frac{13}{75}\); д) \(\frac{22}{7}\); е) \(-\frac{17}{90}\).