3). Вычислите: a) \(\frac{5^8 \cdot 5^7}{5^{12}}\); б) \(\frac{5^{12}}{2^5 \cdot 8}\)

Решение:

1. а)

   \(\frac{5^8 \cdot 5^7}{5^{12}} = \frac{5^{8+7}}{5^{12}} = \frac{5^{15}}{5^{12}} = 5^{15-12} = 5^3 = 125\)

2. б)

   \(\frac{5^{12}}{2^5 \cdot 8} = \frac{5^{12}}{2^5 \cdot 2^3} = \frac{5^{12}}{2^{5+3}} = \frac{5^{12}}{2^8}\)

Ответ: а) 125; б) \(\frac{5^{12}}{2^8}\).