Вычисли значения выражений, используя свойства степени. 1. $$\frac{1}{8^2} \cdot 8^3 =$$ 2. $$5 \div \frac{1}{5^2} =$$ 3. $$8^3 \cdot \frac{1}{2^5} =$$ 4. $$\frac{1}{125^2} \div \frac{1}{5^6} = $$

1. $$\frac{1}{8^2} \cdot 8^3 = \frac{8^3}{8^2} = 8^{3-2} = 8^1 = \mathbf{8}$$
2. $$5 \div \frac{1}{5^2} = 5 \cdot 5^2 = 5^1 \cdot 5^2 = 5^{1+2} = 5^3 = \mathbf{125}$$
3. $$8^3 \cdot \frac{1}{2^5} = (2^3)^3 \cdot \frac{1}{2^5} = 2^9 \cdot \frac{1}{2^5} = \frac{2^9}{2^5} = 2^{9-5} = 2^4 = \mathbf{16}$$
4. $$\frac{1}{125^2} \div \frac{1}{5^6} = \frac{1}{125^2} \cdot 5^6 = \frac{5^6}{(5^3)^2} = \frac{5^6}{5^6} = \mathbf{1}$$