3. Вычислите:

Решение:

1. a) \( \frac{8^{16} \cdot 8^{10}}{8^{24}} = \frac{8^{16+10}}{8^{24}} = \frac{8^{26}}{8^{24}} = 8^{26-24} = 8^2 = 64 \)
2. б) \( \frac{(-5)^3 \cdot (-5)^{10}}{(5^3)^3} = \frac{(-5)^{3+10}}{5^{3 \cdot 3}} = \frac{(-5)^{13}}{5^9} = \frac{-(5^{13})}{5^9} = -5^{13-9} = -5^4 = -625 \)
3. в) \( \frac{2^{10} + 2^9 + 2^8}{2^9 + (4^2)^2} = \frac{2^8(2^2 + 2^1 + 1)}{2^9 + (2^2)^2} = \frac{2^8(4 + 2 + 1)}{2^9 + 2^4} = \frac{2^8 \cdot 7}{2^4(2^5 + 1)} = \frac{2^8 \cdot 7}{2^4(32 + 1)} = \frac{2^8 \cdot 7}{2^4 \cdot 33} = \frac{2^4 \cdot 7}{33} = \frac{16 \cdot 7}{33} = \frac{112}{33} \)

Ответ: a) \(64\); б) \(-625\); в) \(\frac{112}{33}\).