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МатематикаВопрос:
1) 2-9. (22)7 = 2) 4-12. (45)2 = (54)-4 3) (63)-6 5-18 4) = 6-20 2-3.219 5) 3-3.313 = 213 6) 38 1 1 1 1 7) 5-8 56 27 = 8) = 2-10 27 35 10) = 81 9) 이 307 11) = 35.104 1510 12) = 37.59 59.810 13) = 409 (2.3)8 14) = 26.37 15) (5.4)7 56.45-
Ответ:
1) $$2^{-9} \cdot (2^2)^7 = 2^{-9} \cdot 2^{14} = 2^{-9+14} = 2^5 = 32$$.
2) $$4^{-12} \cdot (4^5)^2 = 4^{-12} \cdot 4^{10} = 4^{-12+10} = 4^{-2} = \frac{1}{4^2} = \frac{1}{16}$$.
3) $$\frac{(5^4)^{-4}}{5^{-18}} = \frac{5^{-16}}{5^{-18}} = 5^{-16 - (-18)} = 5^{-16+18} = 5^2 = 25$$.
4) $$\frac{(6^3)^{-6}}{6^{-20}} = \frac{6^{-18}}{6^{-20}} = 6^{-18 - (-20)} = 6^{-18+20} = 6^2 = 36$$.
5) $$\frac{2^{-3} \cdot 2^{19}}{2^{13}} = \frac{2^{-3+19}}{2^{13}} = \frac{2^{16}}{2^{13}} = 2^{16-13} = 2^3 = 8$$.
6) $$\frac{3^{-3} \cdot 3^{13}}{3^8} = \frac{3^{-3+13}}{3^8} = \frac{3^{10}}{3^8} = 3^{10-8} = 3^2 = 9$$.
7) $$\frac{1}{5^{-8}} \cdot \frac{1}{5^6} = 5^8 \cdot 5^{-6} = 5^{8-6} = 5^2 = 25$$.
8) $$\frac{1}{2^{-10}} \cdot \frac{1}{2^7} = 2^{10} \cdot 2^{-7} = 2^{10-7} = 2^3 = 8$$.
9) $$\frac{2^7}{8} = \frac{2^7}{2^3} = 2^{7-3} = 2^4 = 16$$.
10) $$\frac{3^5}{81} = \frac{3^5}{3^4} = 3^{5-4} = 3^1 = 3$$.
11) $$\frac{30^7}{3^5 \cdot 10^4} = \frac{(3 \cdot 10)^7}{3^5 \cdot 10^4} = \frac{3^7 \cdot 10^7}{3^5 \cdot 10^4} = 3^{7-5} \cdot 10^{7-4} = 3^2 \cdot 10^3 = 9 \cdot 1000 = 9000$$.
12) $$\frac{15^{10}}{3^7 \cdot 5^9} = \frac{(3 \cdot 5)^{10}}{3^7 \cdot 5^9} = \frac{3^{10} \cdot 5^{10}}{3^7 \cdot 5^9} = 3^{10-7} \cdot 5^{10-9} = 3^3 \cdot 5^1 = 27 \cdot 5 = 135$$.
13) $$\frac{5^9 \cdot 8^{10}}{40^9} = \frac{5^9 \cdot (2^3)^{10}}{(5 \cdot 2^3)^9} = \frac{5^9 \cdot 2^{30}}{5^9 \cdot 2^{27}} = 5^{9-9} \cdot 2^{30-27} = 5^0 \cdot 2^3 = 1 \cdot 8 = 8$$.
14) $$\frac{(2 \cdot 3)^8}{2^6 \cdot 3^7} = \frac{2^8 \cdot 3^8}{2^6 \cdot 3^7} = 2^{8-6} \cdot 3^{8-7} = 2^2 \cdot 3^1 = 4 \cdot 3 = 12$$.
15) $$\frac{(5 \cdot 4)^7}{5^6 \cdot 4^5} = \frac{(5 \cdot 2^2)^7}{5^6 \cdot (2^2)^5} = \frac{5^7 \cdot 2^{14}}{5^6 \cdot 2^{10}} = 5^{7-6} \cdot 2^{14-10} = 5^1 \cdot 2^4 = 5 \cdot 16 = 80$$.
2) $$4^{-12} \cdot (4^5)^2 = 4^{-12} \cdot 4^{10} = 4^{-12+10} = 4^{-2} = \frac{1}{4^2} = \frac{1}{16}$$.
3) $$\frac{(5^4)^{-4}}{5^{-18}} = \frac{5^{-16}}{5^{-18}} = 5^{-16 - (-18)} = 5^{-16+18} = 5^2 = 25$$.
4) $$\frac{(6^3)^{-6}}{6^{-20}} = \frac{6^{-18}}{6^{-20}} = 6^{-18 - (-20)} = 6^{-18+20} = 6^2 = 36$$.
5) $$\frac{2^{-3} \cdot 2^{19}}{2^{13}} = \frac{2^{-3+19}}{2^{13}} = \frac{2^{16}}{2^{13}} = 2^{16-13} = 2^3 = 8$$.
6) $$\frac{3^{-3} \cdot 3^{13}}{3^8} = \frac{3^{-3+13}}{3^8} = \frac{3^{10}}{3^8} = 3^{10-8} = 3^2 = 9$$.
7) $$\frac{1}{5^{-8}} \cdot \frac{1}{5^6} = 5^8 \cdot 5^{-6} = 5^{8-6} = 5^2 = 25$$.
8) $$\frac{1}{2^{-10}} \cdot \frac{1}{2^7} = 2^{10} \cdot 2^{-7} = 2^{10-7} = 2^3 = 8$$.
9) $$\frac{2^7}{8} = \frac{2^7}{2^3} = 2^{7-3} = 2^4 = 16$$.
10) $$\frac{3^5}{81} = \frac{3^5}{3^4} = 3^{5-4} = 3^1 = 3$$.
11) $$\frac{30^7}{3^5 \cdot 10^4} = \frac{(3 \cdot 10)^7}{3^5 \cdot 10^4} = \frac{3^7 \cdot 10^7}{3^5 \cdot 10^4} = 3^{7-5} \cdot 10^{7-4} = 3^2 \cdot 10^3 = 9 \cdot 1000 = 9000$$.
12) $$\frac{15^{10}}{3^7 \cdot 5^9} = \frac{(3 \cdot 5)^{10}}{3^7 \cdot 5^9} = \frac{3^{10} \cdot 5^{10}}{3^7 \cdot 5^9} = 3^{10-7} \cdot 5^{10-9} = 3^3 \cdot 5^1 = 27 \cdot 5 = 135$$.
13) $$\frac{5^9 \cdot 8^{10}}{40^9} = \frac{5^9 \cdot (2^3)^{10}}{(5 \cdot 2^3)^9} = \frac{5^9 \cdot 2^{30}}{5^9 \cdot 2^{27}} = 5^{9-9} \cdot 2^{30-27} = 5^0 \cdot 2^3 = 1 \cdot 8 = 8$$.
14) $$\frac{(2 \cdot 3)^8}{2^6 \cdot 3^7} = \frac{2^8 \cdot 3^8}{2^6 \cdot 3^7} = 2^{8-6} \cdot 3^{8-7} = 2^2 \cdot 3^1 = 4 \cdot 3 = 12$$.
15) $$\frac{(5 \cdot 4)^7}{5^6 \cdot 4^5} = \frac{(5 \cdot 2^2)^7}{5^6 \cdot (2^2)^5} = \frac{5^7 \cdot 2^{14}}{5^6 \cdot 2^{10}} = 5^{7-6} \cdot 2^{14-10} = 5^1 \cdot 2^4 = 5 \cdot 16 = 80$$.
