1. Вычислите: а) 7/8 ⋅ 9/28; б) 18/19 ⋅ 27/38; в) (2/3)^4 ⋅ (3/2)^4.

а) \[\frac{7}{8} \cdot \frac{9}{28} = \frac{7 \cdot 9}{8 \cdot 28} = \frac{7 \cdot 9}{8 \cdot 4 \cdot 7} = \frac{9}{8 \cdot 4} = \frac{9}{32}\]

б) \[\frac{18}{19} \cdot \frac{27}{38} = \frac{18 \cdot 27}{19 \cdot 38} = \frac{18 \cdot 27}{19 \cdot 2 \cdot 19} = \frac{9 \cdot 27}{19 \cdot 19} = \frac{243}{361}\]

в) \[(\frac{2}{3})^4 \cdot (\frac{3}{2})^4 = \frac{2^4}{3^4} \cdot \frac{3^4}{2^4} = \frac{2^4 \cdot 3^4}{3^4 \cdot 2^4} = 1\]