1. Вычислить: 1) \(\frac{5^{-5.5-8}}{5^{-14}}\); 2) \(\frac{\sqrt[3]{49} \cdot \sqrt[3]{7}}{\sqrt[3]{70}}\)

Решение:

1. \(\frac{5^{-5.5-8}}{5^{-14}} = \frac{5^{-13.5}}{5^{-14}} = 5^{-13.5 - (-14)} = 5^{-13.5 + 14} = 5^{0.5} = \sqrt{5}\)
2. \(\frac{\sqrt[3]{49} \cdot \sqrt[3]{7}}{\sqrt[3]{70}} = \sqrt[3]{\frac{49 \cdot 7}{70}} = \sqrt[3]{\frac{7^2 \cdot 7}{7 \cdot 10}} = \sqrt[3]{\frac{7^3}{10}} = \frac{7}{\sqrt[3]{10}}\).

Ответ: 1) \(\sqrt{5}\); 2) \(\frac{7}{\sqrt[3]{10}}\).