Найти значение выражения, используя свойства степеней: 1) \(3^7\cdot(3^2)^3:3^{10}\); 2) \(5^{20}:(5^2)^5:5^8\); 3) \(\frac{9^4}{3^7}\); 4) \(\frac{8^5}{4^6}\); 5) \(\frac{27^2\cdot9^4}{81^{12}}\); 6) \(\frac{10^{12}}{2^6\cdot5^6}\); 7) \(\frac{5^{16}\cdot3^{16}}{15^{14}}\); 8) \(\frac{12^6}{3^5\cdot4^5}\).

1. \[3^7\cdot(3^2)^3:3^{10}=3^7\cdot3^6:3^{10}=3^3=27.\]
2. \[5^{20}:(5^2)^5:5^8=5^{20}:5^{10}:5^8=5^2=25.\]
3. \[\frac{9^4}{3^7}=\frac{(3^2)^4}{3^7}=3=3.\]
4. \[\frac{8^5}{4^6}=\frac{(2^3)^5}{(2^2)^6}=2^{15-12}=2^3=8.\]
5. \[\frac{27^2\cdot9^4}{81^{12}}=\frac{(3^3)^2\cdot(3^2)^4}{(3^4)^{12}}=3^{6+8-48}=3^{-34}=\frac1{3^{34}}.\]
6. \[\frac{10^{12}}{2^6\cdot5^6}=\frac{(2\cdot5)^{12}}{2^6\cdot5^6}=2^6\cdot5^6=10^6=1\,000\,000.\]
7. \[\frac{5^{16}\cdot3^{16}}{15^{14}}=\frac{15^{16}}{15^{14}}=15^2=225.\]
8. \[\frac{12^6}{3^5\cdot4^5}=\frac{(3\cdot4)^6}{3^5\cdot4^5}=3\cdot4=12.\]

Ответ: 1) 27; 2) 25; 3) 3; 4) 8; 5) \(\frac1{3^{34}}\); 6) 1 000 000; 7) 225; 8) 12.