4. Упростите: 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. \(\dfrac{2^{12}(2\cdot3)^7 3^2}{(2\cdot3^2)^4 2^9}=\dfrac{2^{19}3^9}{2^{13}3^8}=2^6\cdot3=192\).
2. \(\dfrac{2\cdot5^9\cdot3^8\cdot2^4}{(2\cdot5)^7 3^6}=2^{-2}5^2 3^2=\dfrac{225}{4}\).
3. \(\dfrac{3^9 5^7 2^2}{3^8 2^5 5^5}=\dfrac{3\cdot5^2}{2^3}=\dfrac{75}{8}\).
4. \(\dfrac{(2\cdot3)^9 3^4 5^4}{2^3 5^3(2\cdot3^2)^7}=\dfrac{2^9 3^{13}5^4}{2^{10}3^{14}5^3}=\dfrac56\).

Ответ: 1) 192; 2) 225/4; 3) 75/8; 4) 5/6.