284. Вычислите: А) \(\frac{5^{10}\cdot(5^3)^4}{5^{18}}\); Б) \(\frac{3^{34}}{3^{17}\cdot(3^5)^2}\); В) \(\frac{7^{11}}{7^2\cdot(7^4)^3}\); Г) \(\frac{2^{21}\cdot(2^3)^5}{2^{40}}\); Д) \((0,1)^{25}\cdot10^{23}\); Е) \(2,5^{43}\cdot\left(\frac25\right)^{41}\); Ё) \(\left(2\frac23\right)^{11}\cdot0,375^8\); Ж) \(1,4^{21}\cdot\left(\frac57\right)^{19}\).

1. \(\frac{5^{10}\cdot(5^3)^4}{5^{18}}=5^{10+12-18}=5^4=625\).
2. \(\frac{3^{34}}{3^{17}\cdot(3^5)^2}=3^{34-17-10}=3^7=2187\).
3. \(\frac{7^{11}}{7^2\cdot(7^4)^3}=7^{11-2-12}=7^{-3}=\frac1{343}\).
4. \(\frac{2^{21}\cdot(2^3)^5}{2^{40}}=2^{21+15-40}=2^{-4}=\frac1{16}\).
5. \((0,1)^{25}\cdot10^{23}=10^{-25}\cdot10^{23}=10^{-2}=0,01\).
6. \(2,5^{43}\cdot\left(\frac25\right)^{41}=\left(\frac52\right)^{43}\cdot\left(\frac25\right)^{41}=\left(\frac52\right)^2=\frac{25}{4}\).
7. \(\left(2\frac23\right)^{11}\cdot0,375^8=\left(\frac83\right)^{11}\cdot\left(\frac38\right)^8=\left(\frac83\right)^3=\frac{512}{27}\).
8. \(1,4^{21}\cdot\left(\frac57\right)^{19}=\left(\frac75\right)^{21}\cdot\left(\frac57\right)^{19}=\left(\frac75\right)^2=\frac{49}{25}\).

Ответ: А) 625; Б) 2187; В) \(\frac1{343}\); Г) \(\frac1{16}\); Д) 0,01; Е) \(\frac{25}{4}\); Ё) \(\frac{512}{27}\); Ж) \(\frac{49}{25}\).