5. Вычислите: 1) ((0,5)³ · 8⁷ · 12²)/(6³ · 2¹⁵); 2) ((1/4)³ : 9 · 20³)/(18⁴ · 5²).

1. \(\frac{(0.5)^3\cdot8^7\cdot12^2}{6^3\cdot2^{15}}=\frac{2^{-3}\cdot2^{21}\cdot(2^2\cdot3)^2}{(2\cdot3)^3\cdot2^{15}}=\frac{2^4\cdot3^2}{2^3\cdot3^3}=\frac{2}{3}\).
2. \(\frac{(\frac14)^3:9\cdot20^3}{18^4\cdot5^2}=\frac{2^{-6}\cdot3^{-2}\cdot(2^2\cdot5)^3}{(2\cdot3^2)^4\cdot5^2}=\frac{2^{-6+6-8}\cdot5^{3-2}}{3^{2+8}}=\frac{5}{2^8\cdot3^{10}}=\frac{5}{15116544}\).

Ответ: 1) \(\frac{2}{3}\); 2) \(\frac{5}{15116544}\).