237. Вычислите: 1) 100⁵ : 1000²; 2) 3¹⁰ · (3³)⁵ / ((3⁵)⁴ · 3); 3) 4³ · 16² / 2¹²; 4) 45¹⁰ / (5⁸ · 3¹⁹).

1. \(\dfrac{100^5}{1000^2}=\dfrac{10^{10}}{10^6}=10^4=10000\).
2. \(\dfrac{3^{10}\cdot(3^3)^5}{(3^5)^4\cdot3}=3^{10+15-20-1}=3^4=81\).
3. \(\dfrac{4^3\cdot16^2}{2^{12}}=\dfrac{2^6\cdot2^8}{2^{12}}=2^2=4\).
4. \(\dfrac{45^{10}}{5^8\cdot3^{19}}=\dfrac{3^{10}5^{10}}{3^{19}5^8}=\dfrac{5^2}{3^9}=\dfrac{25}{19683}\).

Ответ: 1) 10000; 2) 81; 3) 4; 4) \(\dfrac{25}{19683}\).