Вычислите: 1) \(\frac{20^{15}}{10^{20}}\); 2) \(5^6\cdot125\); 3) \(\left(\frac{3}{5}\right)^5\cdot\left(\frac{5}{3}\right)^5\); 4) \(\frac{(a^6)^3}{(a^6)^3}\); 5) \(\left(\frac{3}{8}\right)^2\).

1. \(\frac{20^{15}}{10^{20}}=\frac{(2\cdot10)^{15}}{10^{20}}=\frac{2^{15}}{10^5}=\frac{32768}{100000}=0.32768\).
2. \(5^6\cdot125=5^6\cdot5^3=5^9=1\,953\,125\).
3. \(\left(\frac{3}{5}\right)^5\cdot\left(\frac{5}{3}\right)^5=\left(\frac{3}{5}\cdot\frac{5}{3}\right)^5=1\).
4. \(\frac{(a^6)^3}{(a^6)^3}=1\), при \(a\ne0\).
5. \(\left(\frac{3}{8}\right)^2=\frac{9}{64}\).

Ответ: 1) 0.32768; 2) 1 953 125; 3) 1; 4) 1; 5) \(\frac{9}{64}\).