3 Вычислите: a) \(\frac{6^7 - 6^{11}}{6^{15}}\) б) \(\frac{8^4 \cdot 8^{13}}{8^{18}} : \frac{3^5 \cdot 3^9}{3^{12} \cdot 9^2}\)

3. Вычислите:

1. a) \( \frac{6^7 - 6^{11}}{6^{15}} = \frac{6^7(1 - 6^4)}{6^{15}} = \frac{1 - 1296}{6^8} = \frac{-1295}{1679616} \)
2. б) \( \frac{8^4 \cdot 8^{13}}{8^{18}} = \frac{8^{4+13}}{8^{18}} = \frac{8^{17}}{8^{18}} = \frac{1}{8} \) \( \frac{3^5 \cdot 3^9}{3^{12} \cdot 9^2} = \frac{3^{5+9}}{3^{12} \cdot (3^2)^2} = \frac{3^{14}}{3^{12} \cdot 3^4} = \frac{3^{14}}{3^{16}} = \frac{1}{3^2} = \frac{1}{9} \) \( \frac{1}{8} : \frac{1}{9} = \frac{1}{8} \cdot 9 = \frac{9}{8} \)

Ответ: а) \( \frac{-1295}{1679616} \); б) \( \frac{9}{8} \).