2. Упростите выражение: a) \(\frac{a}{3b} \cdot \frac{2a}{b^2}\) б) \(\frac{a^2}{3b} \cdot (\frac{b^2}{3a} \cdot \frac{b}{5a})\) в) \(\frac{a^2}{3b} \cdot \frac{b^2}{3a} \cdot \frac{b}{5a}\) г) \(\frac{a^2}{3b} \cdot (\frac{b^2}{3a}) \cdot \frac{b}{5a}\)

Решение:

а) \(\frac{a}{3b} \cdot \frac{2a}{b^2} = \frac{a · 2a}{3b · b^2} = \frac{2a^2}{3b^3}\)

б) \(\frac{a^2}{3b} \cdot (\frac{b^2}{3a} \cdot \frac{b}{5a}) = \frac{a^2}{3b} \cdot \frac{b^3}{15a^2} = \frac{a^2 · b^3}{3b · 15a^2} = \frac{b^2}{45}\)

в) \(\frac{a^2}{3b} \cdot \frac{b^2}{3a} \cdot \frac{b}{5a} = \frac{a^2 · b^2 · b}{3b · 3a · 5a} = \frac{a^2b^3}{45a^2b} = \frac{b^2}{45}\)

г) \(\frac{a^2}{3b} \cdot (\frac{b^2}{3a}) \cdot \frac{b}{5a} = \frac{a^2b^2}{9ab} \cdot \frac{b}{5a} = \frac{ab}{9} \cdot \frac{b}{5a} = \frac{ab^2}{45a} = \frac{b^2}{45}\)

Ответ: а) \(\frac{2a^2}{3b^3}\); б) \(\frac{b^2}{45}\); в) \(\frac{b^2}{45}\); г) \(\frac{b^2}{45}\).