Найдите значения выражений: 1. 24^4 / (3^2 * 8^3), 2. (12^11 * 2^9) / 24^9, 3. 3^7 / 81...

Для решения задач со степенями используем свойства: $a^n \cdot a^m = a^{n+m}$, $a^n : a^m = a^{n-m}$, $(a^n)^m = a^{n \cdot m}$, $(a \cdot b)^n = a^n \cdot b^n$. 1. $\frac{24^4}{3^2 \cdot 8^3} = \frac{(3 \cdot 8)^4}{3^2 \cdot 8^3} = \frac{3^4 \cdot 8^4}{3^2 \cdot 8^3} = 3^{4-2} \cdot 8^{4-3} = 3^2 \cdot 8^1 = 9 \cdot 8 = 72$ 2. $\frac{12^{11} \cdot 2^9}{24^9} = \frac{12^{11} \cdot 2^9}{(12 \cdot 2)^9} = \frac{12^{11} \cdot 2^9}{12^9 \cdot 2^9} = 12^{11-9} = 12^2 = 144$ 3. $\frac{3^7}{81} = \frac{3^7}{3^4} = 3^{7-4} = 3^3 = 27$ 4. $\frac{27^5}{9^6} = \frac{(3^3)^5}{(3^2)^6} = \frac{3^{15}}{3^{12}} = 3^{15-12} = 3^3 = 27$ 5. $\frac{10^6}{2^5 \cdot 5^4} = \frac{(2 \cdot 5)^6}{2^5 \cdot 5^4} = \frac{2^6 \cdot 5^6}{2^5 \cdot 5^4} = 2^{6-5} \cdot 5^{6-4} = 2^1 \cdot 5^2 = 2 \cdot 25 = 50$ 16. $\frac{81^5}{27^6} = \frac{(3^4)^5}{(3^3)^6} = \frac{3^{20}}{3^{18}} = 3^{20-18} = 3^2 = 9$ 17. $\frac{5^5}{25} = \frac{5^5}{5^2} = 5^{5-2} = 5^3 = 125$ 18. $\frac{8^8}{4^{10}} = \frac{(2^3)^8}{(2^2)^{10}} = \frac{2^{24}}{2^{20}} = 2^{24-20} = 2^4 = 16$ 19. $\frac{64^2}{16^3} = \frac{(4^3)^2}{(4^2)^3} = \frac{4^6}{4^6} = 1$ 20. $\frac{3^6}{9} = \frac{3^6}{3^2} = 3^{6-2} = 3^4 = 81$ 21. $\frac{4^4}{64} = \frac{4^4}{4^3} = 4^{4-3} = 4^1 = 4$ 22. $\frac{(2 \cdot 6)^7}{2^5 \cdot 6^6} = \frac{2^7 \cdot 6^7}{2^5 \cdot 6^6} = 2^{7-5} \cdot 6^{7-6} = 2^2 \cdot 6^1 = 4 \cdot 6 = 24$ 33. $\frac{2^9}{16} = \frac{2^9}{2^4} = 2^{9-4} = 2^5 = 32$ 34. $\frac{32^3}{4^7} = \frac{(2^5)^3}{(2^2)^7} = \frac{2^{15}}{2^{14}} = 2^{15-14} = 2^1 = 2$ 35. $\frac{32^5}{8^8} = \frac{(2^5)^5}{(2^3)^8} = \frac{2^{25}}{2^{24}} = 2^{25-24} = 2^1 = 2$ 36. $\frac{32^2}{16^3} = \frac{(2^5)^2}{(2^4)^3} = \frac{2^{10}}{2^{12}} = \frac{1}{2^2} = \frac{1}{4} = 0,25$ 37. $\frac{2^7}{32} = \frac{2^7}{2^5} = 2^{7-5} = 2^2 = 4$ 38. $\frac{(3 \cdot 6)^4}{3^2 \cdot 6^3} = \frac{3^4 \cdot 6^4}{3^2 \cdot 6^3} = 3^{4-2} \cdot 6^{4-3} = 3^2 \cdot 6^1 = 9 \cdot 6 = 54$ 39. $\frac{2^7}{8} = \frac{2^7}{2^3} = 2^{7-3} = 2^4 = 16$