Вычислите: а) \(\frac{2^{12}-2^9}{7\cdot2^8}\); б) \(\frac{2\cdot5^{10}-5^{11}}{6\cdot5^{11}}\); в) \(\frac{3^{12}+3^{10}}{3^8}\); г) \(\frac{5^8+5^6}{2\cdot5^7}\).

1. \(\displaystyle \frac{2^{12}-2^9}{7\cdot2^8}=\frac{2^9(2^3-1)}{7\cdot2^8}=\frac{2^9\cdot7}{7\cdot2^8}=2\).
2. \(\displaystyle \frac{2\cdot5^{10}-5^{11}}{6\cdot5^{11}}=\frac{5^{10}(2-5)}{6\cdot5^{11}}=\frac{-3}{6\cdot5}=-\frac{1}{10}\).
3. \(\displaystyle \frac{3^{12}+3^{10}}{3^8}=\frac{3^{10}(3^2+1)}{3^8}=3^2\cdot10=90\).
4. \(\displaystyle \frac{5^8+5^6}{2\cdot5^7}=\frac{5^6(5^2+1)}{2\cdot5^7}=\frac{26}{2\cdot5}=\frac{13}{5}\).

Ответ: а) \(2\); б) \(-\frac{1}{10}\); в) \(90\); г) \(\frac{13}{5}\).