2. Вычислите: a) \(\frac{4}{45} : (\frac{12}{25} - \frac{4}{15}) + \frac{15}{16} \cdot \frac{4}{15}\); б) \((1 - \frac{1}{2})^3 : (\frac{1}{3} - \frac{1}{4})^2 \cdot (\frac{1}{6})^2\).

Вычисляем:

а) \(\frac{4}{45} : (\frac{12}{25} - \frac{4}{15}) + \frac{15}{16} \cdot \frac{4}{15} = \frac{4}{45} : (\frac{36}{75} - \frac{20}{75}) + \frac{60}{240} = \frac{4}{45} : \frac{16}{75} + \frac{1}{4} = \frac{4}{45} \cdot \frac{75}{16} + \frac{1}{4} = \frac{300}{720} + \frac{1}{4} = \frac{5}{12} + \frac{1}{4} = \frac{5}{12} + \frac{3}{12} = \frac{8}{12} = \frac{2}{3}\)

б) \((1 - \frac{1}{2})^3 : (\frac{1}{3} - \frac{1}{4})^2 \cdot (\frac{1}{6})^2 = (\frac{1}{2})^3 : (\frac{4}{12} - \frac{3}{12})^2 \cdot \frac{1}{36} = \frac{1}{8} : (\frac{1}{12})^2 \cdot \frac{1}{36} = \frac{1}{8} : \frac{1}{144} \cdot \frac{1}{36} = \frac{1}{8} \cdot 144 \cdot \frac{1}{36} = \frac{144}{8} \cdot \frac{1}{36} = 18 \cdot \frac{1}{36} = \frac{18}{36} = \frac{1}{2}\)

Ответ: а) \(\frac{2}{3}\); б) \(\frac{1}{2}\).