Вычислите: $(\frac{5}{7})^2 \cdot \frac{7}{15}$

1) $$\left(\frac{5}{7}\right)^2 \cdot \frac{7}{15} = \frac{25}{49} \cdot \frac{7}{15} = \frac{25 \cdot 7}{49 \cdot 15} = \frac{5 \cdot 1}{7 \cdot 3} = \frac{5}{21}$$ **Ответ:** $\frac{5}{21}$ 2) $$\left(\frac{3}{4}\right)^2 \cdot \frac{32}{45} = \frac{9}{16} \cdot \frac{32}{45} = \frac{9 \cdot 32}{16 \cdot 45} = \frac{1 \cdot 2}{1 \cdot 5} = \frac{2}{5}$$ **Ответ:** $\frac{2}{5}$ 3) $$\left(\frac{1}{2}\right)^2 \cdot \frac{4}{5} = \frac{1}{4} \cdot \frac{4}{5} = \frac{1 \cdot 4}{4 \cdot 5} = \frac{1}{5}$$ **Ответ:** $\frac{1}{5}$ 4) $$\left(2\frac{5}{7}\right)^2 \cdot \frac{14}{19} = \left(\frac{19}{7}\right)^2 \cdot \frac{14}{19} = \frac{19^2}{7^2} \cdot \frac{14}{19} = \frac{19 \cdot 19}{49} \cdot \frac{14}{19} = \frac{19 \cdot 14}{49} = \frac{19 \cdot 2}{7} = \frac{38}{7} = 5\frac{3}{7}$$ **Ответ:** $5\frac{3}{7}$ 5) $$\left(2\frac{1}{3}\right)^2 \cdot \frac{27}{98} = \left(\frac{7}{3}\right)^2 \cdot \frac{27}{98} = \frac{49}{9} \cdot \frac{27}{98} = \frac{49 \cdot 27}{9 \cdot 98} = \frac{1 \cdot 3}{1 \cdot 2} = \frac{3}{2} = 1\frac{1}{2}$$ **Ответ:** $1\frac{1}{2}$ 6) $$\left(\frac{8}{11}\right)^2 \cdot \frac{11}{32} = \frac{64}{121} \cdot \frac{11}{32} = \frac{64 \cdot 11}{121 \cdot 32} = \frac{2 \cdot 1}{11 \cdot 1} = \frac{2}{11}$$ **Ответ:** $\frac{2}{11}$ 7) $$\left(\frac{3}{10}\right)^2 \cdot \frac{5}{6} = \frac{9}{100} \cdot \frac{5}{6} = \frac{9 \cdot 5}{100 \cdot 6} = \frac{3 \cdot 1}{20 \cdot 2} = \frac{3}{40}$$ **Ответ:** $\frac{3}{40}$ 8) $$\left(\frac{2}{3}\right)^2 \cdot \frac{15}{24} = \frac{4}{9} \cdot \frac{15}{24} = \frac{4 \cdot 15}{9 \cdot 24} = \frac{1 \cdot 5}{3 \cdot 6} = \frac{5}{18}$$ **Ответ:** $\frac{5}{18}$