Найдите значение выражения: 1 (22.24)7 (2.26)6 2 (33.35)6 (3.38)5 3 (3.10)8 36.107 4 (5.7)6 54.76 5 (a³)5.a6 a19 при а=5 6 (a7)3.a10 a28 при а =4 7 (a3)6.a3 a17 при а = 3 8 (a³)4.a12 a21 при а =5 9 (a4)5 a18 при а=6 10 (a8)2 a11 при а=2 11 (a8)2 a13 при а=5 12 (a3)5 a11 при а=3 13 207 46.55 14 244 32.83 15 286 44.75 16 306 34.105

1. \[\frac{(2^2 \cdot 2^4)^7}{(2 \cdot 2^6)^6} = \frac{(2^{2+4})^7}{(2^{1+6})^6} = \frac{(2^6)^7}{(2^7)^6} = \frac{2^{6 \cdot 7}}{2^{7 \cdot 6}} = \frac{2^{42}}{2^{42}} = 1\]

2. \[\frac{(3^3 \cdot 3^5)^6}{(3 \cdot 3^8)^5} = \frac{(3^{3+5})^6}{(3^{1+8})^5} = \frac{(3^8)^6}{(3^9)^5} = \frac{3^{8 \cdot 6}}{3^{9 \cdot 5}} = \frac{3^{48}}{3^{45}} = 3^{48-45} = 3^3 = 27\]

3. \[\frac{(3 \cdot 10)^8}{3^6 \cdot 10^7} = \frac{3^8 \cdot 10^8}{3^6 \cdot 10^7} = 3^{8-6} \cdot 10^{8-7} = 3^2 \cdot 10^1 = 9 \cdot 10 = 90\]

4. \[\frac{(5 \cdot 7)^6}{5^4 \cdot 7^6} = \frac{5^6 \cdot 7^6}{5^4 \cdot 7^6} = 5^{6-4} \cdot 7^{6-6} = 5^2 \cdot 7^0 = 25 \cdot 1 = 25\]

5. \[\frac{(a^3)^5 \cdot a^6}{a^{19}} = \frac{a^{3 \cdot 5} \cdot a^6}{a^{19}} = \frac{a^{15} \cdot a^6}{a^{19}} = \frac{a^{15+6}}{a^{19}} = \frac{a^{21}}{a^{19}} = a^{21-19} = a^2 = 5^2 = 25\]

6. \[\frac{(a^7)^3 \cdot a^{10}}{a^{28}} = \frac{a^{7 \cdot 3} \cdot a^{10}}{a^{28}} = \frac{a^{21} \cdot a^{10}}{a^{28}} = \frac{a^{21+10}}{a^{28}} = \frac{a^{31}}{a^{28}} = a^{31-28} = a^3 = 4^3 = 64\]

7. \[\frac{(a^3)^6 \cdot a^3}{a^{17}} = \frac{a^{3 \cdot 6} \cdot a^3}{a^{17}} = \frac{a^{18} \cdot a^3}{a^{17}} = \frac{a^{18+3}}{a^{17}} = \frac{a^{21}}{a^{17}} = a^{21-17} = a^4 = 3^4 = 81\]

8. \[\frac{(a^3)^4 \cdot a^{12}}{a^{21}} = \frac{a^{3 \cdot 4} \cdot a^{12}}{a^{21}} = \frac{a^{12} \cdot a^{12}}{a^{21}} = \frac{a^{12+12}}{a^{21}} = \frac{a^{24}}{a^{21}} = a^{24-21} = a^3 = 5^3 = 125\]

9. \[\frac{(a^4)^5}{a^{18}} = \frac{a^{4 \cdot 5}}{a^{18}} = \frac{a^{20}}{a^{18}} = a^{20-18} = a^2 = 6^2 = 36\]

10. \[\frac{(a^8)^2}{a^{11}} = \frac{a^{8 \cdot 2}}{a^{11}} = \frac{a^{16}}{a^{11}} = a^{16-11} = a^5 = 2^5 = 32\]

11. \[\frac{(a^8)^2}{a^{13}} = \frac{a^{8 \cdot 2}}{a^{13}} = \frac{a^{16}}{a^{13}} = a^{16-13} = a^3 = 5^3 = 125\]

12. \[\frac{(a^3)^5}{a^{11}} = \frac{a^{3 \cdot 5}}{a^{11}} = \frac{a^{15}}{a^{11}} = a^{15-11} = a^4 = 3^4 = 81\]

13. \[\frac{20^7}{4^6 \cdot 5^5} = \frac{(4 \cdot 5)^7}{4^6 \cdot 5^5} = \frac{4^7 \cdot 5^7}{4^6 \cdot 5^5} = 4^{7-6} \cdot 5^{7-5} = 4^1 \cdot 5^2 = 4 \cdot 25 = 100\]

14. \[\frac{24^4}{3^2 \cdot 8^3} = \frac{(3 \cdot 8)^4}{3^2 \cdot 8^3} = \frac{3^4 \cdot 8^4}{3^2 \cdot 8^3} = 3^{4-2} \cdot 8^{4-3} = 3^2 \cdot 8^1 = 9 \cdot 8 = 72\]

15. \[\frac{28^6}{4^4 \cdot 7^5} = \frac{(4 \cdot 7)^6}{4^4 \cdot 7^5} = \frac{4^6 \cdot 7^6}{4^4 \cdot 7^5} = 4^{6-4} \cdot 7^{6-5} = 4^2 \cdot 7^1 = 16 \cdot 7 = 112\]

16. \[\frac{30^6}{3^4 \cdot 10^5} = \frac{(3 \cdot 10)^6}{3^4 \cdot 10^5} = \frac{3^6 \cdot 10^6}{3^4 \cdot 10^5} = 3^{6-4} \cdot 10^{6-5} = 3^2 \cdot 10^1 = 9 \cdot 10 = 90\]