2. Вычислите: a) \frac{6}{11}⋅\frac{5}{9}=\frac{6⋅5}{11⋅9} = = ; б) (\frac{2}{5})^2 = \frac{2⋅2}{5⋅5} = = ; в) (1\frac{1}{3})^3 = \frac{4}{3}⋅\frac{4}{3}⋅\frac{4}{3} = \frac{4⋅4⋅4}{3⋅3⋅3} = = ; г) 3⋅\frac{7}{13} = \frac{3}{1}⋅\frac{7}{13} = = = ; д) \frac{4}{9}⋅5=\frac{4}{9}⋅\frac{5}{1} = = .

Ответ: а) \(\frac{10}{33}\); б) \(\frac{4}{25}\); в) \(\frac{64}{27}\); г) \(\frac{21}{13}\); д) \(\frac{20}{9}\)

Решение:

a) \(\frac{6}{11} \cdot \frac{5}{9} = \frac{6 \cdot 5}{11 \cdot 9} = \frac{2 \cdot 5}{11 \cdot 3} = \frac{10}{33}\)

б) \((\frac{2}{5})^2 = \frac{2 \cdot 2}{5 \cdot 5} = \frac{4}{25}\)

в) \((1\frac{1}{3})^3 = (\frac{4}{3})^3 = \frac{4 \cdot 4 \cdot 4}{3 \cdot 3 \cdot 3} = \frac{64}{27} = 2\frac{10}{27}\)

г) \(3 \cdot \frac{7}{13} = \frac{3}{1} \cdot \frac{7}{13} = \frac{3 \cdot 7}{1 \cdot 13} = \frac{21}{13} = 1\frac{8}{13}\)

д) \(\frac{4}{9} \cdot 5 = \frac{4}{9} \cdot \frac{5}{1} = \frac{4 \cdot 5}{9 \cdot 1} = \frac{20}{9} = 2\frac{2}{9}\)

Ответ: а) \(\frac{10}{33}\); б) \(\frac{4}{25}\); в) \(\frac{64}{27}\); г) \(\frac{21}{13}\); д) \(\frac{20}{9}\)