4. 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) \((2^4)^3\cdot6^7\cdot3^2/(18^4\cdot2^9)=2^{12}2^7 3^7 3^2/(2^8 3^8 2^9)=3\).

2) \(2\cdot(5^3)^3\cdot9^4\cdot4^2/(10^7\cdot3^6)=2\cdot5^9\cdot3^8\cdot2^4/(2^7 5^7 3^7)=2^{-2}\cdot5^2\cdot3=\frac{75}{4}\).

3) \((3^3)^3\cdot5^7\cdot2^2/(81^2\cdot10^5)=3^9 5^7 2^2/(3^8\cdot2^5 5^5)=15/2\).

4) \((6^3)^3\cdot9^2\cdot(5^2)^2/(1000\cdot18^7)=2^9 3^9\cdot3^4\cdot5^4/(2^3 5^3\cdot2^7 3^{14})=5\).

Ответ: 1) 3; 2) \(\frac{75}{4}\); 3) \(\frac{15}{2}\); 4) 5.