Упростите: 1) 4⁵/16; 2) 2⁷/8; 3) 4⁴/64; 4) 3⁵/27; 5) 5³/25; 6) 81⁵/27⁶; 7) 8³/4⁴; 8) 125³/25⁴; 9) 16³/64²; 10) 28⁶/(4⁴ · 7⁵); 11) 20⁷/(4⁸ · 5⁵); 12) 6⁷/(2⁶ · 3⁵); 13) (4⁸ · 11¹⁰)/44⁸; 14) (7⁸ · 10⁶)/70⁶; 15) (5⁹ · 8¹¹)/40⁹.

Используем свойства степеней: представляем числа через одинаковые основания и сокращаем степени.

1. \(\frac{4^5}{16}=\frac{4^5}{4^2}=4^3=64\).
2. \(\frac{2^7}{8}=\frac{2^7}{2^3}=2^4=16\).
3. \(\frac{4^4}{64}=\frac{4^4}{4^3}=4\).
4. \(\frac{3^5}{27}=\frac{3^5}{3^3}=3^2=9\).
5. \(\frac{5^3}{25}=\frac{5^3}{5^2}=5\).
6. \(\frac{81^5}{27^6}=\frac{(3^4)^5}{(3^3)^6}=3^{20-18}=3^2=9\).
7. \(\frac{8^3}{4^4}=\frac{(2^3)^3}{(2^2)^4}=2^{9-8}=2\).
8. \(\frac{125^3}{25^4}=\frac{(5^3)^3}{(5^2)^4}=5^{9-8}=5\).
9. \(\frac{16^3}{64^2}=\frac{(2^4)^3}{(2^6)^2}=2^{12-12}=1\).
10. \(\frac{28^6}{4^4\cdot7^5}=\frac{4^6\cdot7^6}{4^4\cdot7^5}=4^2\cdot7=112\).
11. \(\frac{20^7}{4^8\cdot5^5}=\frac{4^7\cdot5^7}{4^8\cdot5^5}=\frac{5^2}{4}=\frac{25}{4}\).
12. \(\frac{6^7}{2^6\cdot3^5}=\frac{2^7\cdot3^7}{2^6\cdot3^5}=2\cdot3^2=18\).
13. \(\frac{4^8\cdot11^{10}}{44^8}=\frac{4^8\cdot11^{10}}{4^8\cdot11^8}=11^2=121\).
14. \(\frac{7^8\cdot10^6}{70^6}=\frac{7^8\cdot10^6}{7^6\cdot10^6}=7^2=49\).
15. \(\frac{5^9\cdot8^{11}}{40^9}=\frac{5^9\cdot8^9\cdot8^2}{(5\cdot8)^9}=8^2=64\).