64. Найдите значение выражения: 1) (5^9 · 13^9) / 65^8; 2) 24^7 / (8^6 · 3^6); 3) (4^10 · 11^8) / 44^8; 4) 15^12 / (3^12 · 5^10); 5) (2^20 · 3^11) / 72^6; 6) 24^3 / 18^4.

1. \(\dfrac{5^9 \cdot 13^9}{65^8} = \dfrac{(5 \cdot 13)^9}{65^8} = \dfrac{65^9}{65^8} = 65\).
2. \(\dfrac{24^7}{8^6 \cdot 3^6} = \dfrac{24^7}{(8 \cdot 3)^6} = \dfrac{24^7}{24^6} = 24\).
3. \(\dfrac{4^{10} \cdot 11^8}{44^8} = \dfrac{4^{10} \cdot 11^8}{(4 \cdot 11)^8} = 4^2 = 16\).
4. \(\dfrac{15^{12}}{3^{12} \cdot 5^{10}} = \dfrac{3^{12} \cdot 5^{12}}{3^{12} \cdot 5^{10}} = 5^2 = 25\).
5. \(\dfrac{2^{20} \cdot 3^{11}}{72^6} = \dfrac{2^{20} \cdot 3^{11}}{(2^3 \cdot 3^2)^6} = \dfrac{2^{20} \cdot 3^{11}}{2^{18} \cdot 3^{12}} = \dfrac{2^2}{3} = \dfrac{4}{3}\).
6. \(\dfrac{24^3}{18^4} = \dfrac{(2^3 \cdot 3)^3}{(2 \cdot 3^2)^4} = \dfrac{2^9 \cdot 3^3}{2^4 \cdot 3^8} = \dfrac{2^5}{3^5} = \dfrac{32}{243}\).

Ответ: 1) 65; 2) 24; 3) 16; 4) 25; 5) \(\dfrac{4}{3}\); 6) \(\dfrac{32}{243}\).