Разбираемся с каждым примером по порядку. Тут нужно сокращать дроби, чтобы упростить выражение.
1) \(\frac{9}{2a} \cdot \frac{5a}{3} = \frac{9 \cdot 5a}{2a \cdot 3} = \frac{45a}{6a} = \frac{15}{2}\)
2) \(\frac{5a}{8y} \cdot \frac{7}{10} = \frac{5a \cdot 7}{8y \cdot 10} = \frac{35a}{80y} = \frac{7a}{16y}\)
3) \(\frac{b^2}{10} \cdot \frac{5}{b} = \frac{b^2 \cdot 5}{10 \cdot b} = \frac{5b^2}{10b} = \frac{b}{2}\)
4) \(\frac{12a^2}{25} \cdot \frac{15}{8x^2} = \frac{12a^2 \cdot 15}{25 \cdot 8x^2} = \frac{180a^2}{200x^2} = \frac{9a^2}{10x^2}\)
5) \(\frac{5}{3p} \cdot \frac{2b}{3} = \frac{5 \cdot 2b}{3p \cdot 3} = \frac{10b}{9p}\)
6) \(\frac{3x}{4} \cdot \frac{1}{x} = \frac{3x \cdot 1}{4 \cdot x} = \frac{3x}{4x} = \frac{3}{4}\)
7) \(\frac{3b^2}{10} \cdot \frac{15}{b^3} = \frac{3b^2 \cdot 15}{10 \cdot b^3} = \frac{45b^2}{10b^3} = \frac{9}{2b}\)
8) \(\frac{16x^3}{35} \cdot \frac{5}{8x^3} = \frac{16x^3 \cdot 5}{35 \cdot 8x^3} = \frac{80x^3}{280x^3} = \frac{2}{7}\)
9) \(\frac{5a}{8y} \cdot \frac{7}{10} = \frac{5a \cdot 7}{8y \cdot 10} = \frac{35a}{80y} = \frac{7a}{16y}\)
10) \(\frac{9}{2a} \cdot \frac{5a}{3} = \frac{9 \cdot 5a}{2a \cdot 3} = \frac{45a}{6a} = \frac{15}{2}\)
11) \(\frac{18c^3}{c^4} \cdot \frac{3}{24} = \frac{18c^3 \cdot 3}{c^4 \cdot 24} = \frac{54c^3}{24c^4} = \frac{9}{4c}\)
12) \(\frac{3}{4a^3} \cdot \frac{16a^2}{9} = \frac{3 \cdot 16a^2}{4a^3 \cdot 9} = \frac{48a^2}{36a^3} = \frac{4}{3a}\)
13) \(\frac{15x^3}{4} \cdot \frac{12}{5x} = \frac{15x^3 \cdot 12}{4 \cdot 5x} = \frac{180x^3}{20x} = 9x^2\)
14) \(\frac{15}{3ab} \cdot \frac{12b^3}{3} = \frac{15 \cdot 12b^3}{3ab \cdot 3} = \frac{180b^3}{9ab} = \frac{20b^2}{a}\)
15) \(\frac{18c^3}{c^4} \cdot \frac{3}{24} = \frac{18c^3 \cdot 3}{c^4 \cdot 24} = \frac{54c^3}{24c^4} = \frac{9}{4c}\)