4. 1) ((2⁴)³ · 6⁷ · 3²)/(18⁴ · 2⁹); 3) ((3³)³ · 5⁷ · 2²)/(81² · 10⁵);

1) \(\frac{(2^4)^3\cdot6^7\cdot3^2}{18^4\cdot2^9}=\frac{2^{12}\cdot(2\cdot3)^7\cdot3^2}{(2\cdot3^2)^4\cdot2^9}=\frac{2^{19}\cdot3^9}{2^{13}\cdot3^8}=2^6\cdot3=192\).

3) \(\frac{(3^3)^3\cdot5^7\cdot2^2}{81^2\cdot10^5}=\frac{3^9\cdot5^7\cdot2^2}{(3^4)^2\cdot(2\cdot5)^5}=\frac{3^9\cdot5^7\cdot2^2}{3^8\cdot2^5\cdot5^5}=\frac{3^1\cdot5^2}{2^3}=\frac{75}{8}\).

Ответ: 1) 192; 3) \(\frac{75}{8}\).