2.395. Выполните действия: а) 27/35 · 7/9 − 9/24 · 6/45; б) 1 41/44 · 11/17 − 27/40 · 5/18; в) 12 1/10 · 2 4/11 + 2 24/31 · 7 3/4; г) 13 2/7 − 5 5/8 · (1 2/9 − 39/45); д) (3/5)^3; е) (7/8)^2.

а) \(\frac{27}{35}\cdot\frac{7}{9}-\frac{9}{24}\cdot\frac{6}{45}=\frac{3}{5}-\frac{1}{20}=\frac{12}{20}-\frac{1}{20}=\frac{11}{20}\).

б) \(1\frac{41}{44}=\frac{85}{44}\), поэтому
\(\frac{85}{44}\cdot\frac{11}{17}-\frac{27}{40}\cdot\frac{5}{18}=\frac{5}{4}-\frac{3}{16}=\frac{20}{16}-\frac{3}{16}=\frac{17}{16}=1\frac{1}{16}\).

в) \(12\frac{1}{10}=\frac{121}{10}\), \(2\frac{4}{11}=\frac{26}{11}\), \(2\frac{24}{31}=\frac{86}{31}\), \(7\frac{3}{4}=\frac{31}{4}\).

\(\frac{121}{10}\cdot\frac{26}{11}+\frac{86}{31}\cdot\frac{31}{4}=\frac{143}{5}+\frac{43}{2}=\frac{286}{10}+\frac{215}{10}=\frac{501}{10}=50\frac{1}{10}\).

г) \(1\frac{2}{9}-\frac{39}{45}=\frac{11}{9}-\frac{13}{15}=\frac{55}{45}-\frac{39}{45}=\frac{16}{45}\).

Тогда \(13\frac{2}{7}-5\frac{5}{8}\cdot\frac{16}{45}=13\frac{2}{7}-\frac{45}{8}\cdot\frac{16}{45}=13\frac{2}{7}-2=11\frac{2}{7}\).

д) \(\left(\frac{3}{5}\right)^3=\frac{3^3}{5^3}=\frac{27}{125}\).

е) \(\left(\frac{7}{8}\right)^2=\frac{7^2}{8^2}=\frac{49}{64}\).

Ответ: а) \(\frac{11}{20}\); б) \(1\frac{1}{16}\); в) \(50\frac{1}{10}\); г) \(11\frac{2}{7}\); д) \(\frac{27}{125}\); е) \(\frac{49}{64}\).