10. Найдите значение выражения 1 \frac{4^5}{64^2}; 2 \frac{127}{2^5\cdot6^6}; 3 \frac{8^{11}\cdot9^{13}}{72^{11}}; 4 (5\cdot8)^9 \frac{}{5^6\cdot8^9}; 5 7^{-13}\cdot(7^5)^3; 7 \frac{1}{3^{-18}}\cdot \frac{1}{3^{15}}; 6 \frac{(10^4)^{-6}}{10^{-27}}; 8 \frac{6^{-8}\cdot6^{21}}{6^{10}};

Ответ: 1) 4; 2) 1; 3) 81; 4) 125; 5) 7^2=49; 6) 10^{-24+27}=10^3=1000; 7) 27; 8) 6^3=216

1. \frac{4^5}{64^2} = \frac{4^5}{(4^3)^2} = \frac{4^5}{4^6} = 4^{5-6} = 4^{-1} = \frac{1}{4}
2. \frac{127}{2^5 \cdot 6^6} = \frac{2^7}{2^5 \cdot (2\cdot3)^6} = \frac{2^7}{2^5 \cdot 2^6 \cdot 3^6} = \frac{2^7}{2^{11} \cdot 3^6} = \frac{2^7}{(2\cdot3)^6} = \frac{128}{32*46656}
3. \frac{8^{11} \cdot 9^{13}}{72^{11}} = \frac{8^{11} \cdot 9^{13}}{(8 \cdot 9)^{11}} = \frac{8^{11} \cdot 9^{13}}{8^{11} \cdot 9^{11}} = 9^{13-11} = 9^2 = 81
4. \frac{(5 \cdot 8)^9}{5^6 \cdot 8^9} = \frac{5^9 \cdot 8^9}{5^6 \cdot 8^9} = 5^{9-6} = 5^3 = 125
5. 7^{-13} \cdot (7^5)^3 = 7^{-13} \cdot 7^{15} = 7^{-13+15} = 7^2 = 49
6. \frac{(10^4)^{-6}}{10^{-27}} = \frac{10^{-24}}{10^{-27}} = 10^{-24 - (-27)} = 10^{-24+27} = 10^3 = 1000
7. \frac{1}{3^{-18}} \cdot \frac{1}{3^{15}} = 3^{18} \cdot 3^{-15} = 3^{18-15} = 3^3 = 27
8. \frac{6^{-8} \cdot 6^{21}}{6^{10}} = \frac{6^{-8+21}}{6^{10}} = \frac{6^{13}}{6^{10}} = 6^{13-10} = 6^3 = 216

Ответ: 1) 1/4; 2) \frac{128}{32*46656}; 3) 81; 4) 125; 5) 7^2=49; 6) 10^{-24+27}=10^3=1000; 7) 27; 8) 6^3=216