4. Вычислите: 1) ((2⁴)³ · 6⁷ · 3²)/(18⁴ · 2⁹); 2) (2 · (5³)³ · 9⁴ · 4²)/(10⁷ · 3⁶); 3) ((3³)³ · 5⁷ · 2²)/(81² · 10⁵); 4) ((6³)³ · 9² · (5²)²)/(1000 · 18⁷).

1. \(\frac{(2^4)^3\cdot6^7\cdot3^2}{18^4\cdot2^9}=\frac{2^{12}\cdot2^7\cdot3^7\cdot3^2}{2^8\cdot3^8\cdot2^9}=2^2\cdot3=12\).
2. \(\frac{2\cdot(5^3)^3\cdot9^4\cdot4^2}{10^7\cdot3^6}=\frac{2\cdot5^9\cdot3^8\cdot2^4}{2^7\cdot5^7\cdot3^6}=2^{-2}\cdot5^2\cdot3^2=\frac{225}{4}\).
3. \(\frac{(3^3)^3\cdot5^7\cdot2^2}{81^2\cdot10^5}=\frac{3^9\cdot5^7\cdot2^2}{3^8\cdot2^5\cdot5^5}=\frac{3^1\cdot5^2}{2^3}=\frac{75}{8}\).
4. \(\frac{(6^3)^3\cdot9^2\cdot(5^2)^2}{1000\cdot18^7}=\frac{2^9\cdot3^9\cdot3^4\cdot5^4}{2^3\cdot5^3\cdot2^7\cdot3^{14}}=\frac{5}{2}\).

Ответ: 1) 12; 2) \(\frac{225}{4}\); 3) \(\frac{75}{8}\); 4) \(\frac{5}{2}\).