Решение:

1. $$\sqrt{0,49} = 0,7$$
2. $$\sqrt[3]{64} = 4$$
3. $$-2\sqrt[3]{\frac{10}{27}} = -2 \cdot \frac{\sqrt[3]{10}}{3} = -\frac{2\sqrt[3]{10}}{3}$$
4. $$0,5\sqrt[4]{81} = 0,5 \cdot 3 = 1,5$$
5. $$\sqrt[4]{\frac{81}{16}} + 3\sqrt[3]{-\frac{1}{27}} = \frac{3}{2} + 3 \cdot \left(-\frac{1}{3}\right) = \frac{3}{2} - 1 = \frac{1}{2} = 0,5$$
6. $$(2\sqrt[3]{6})^3 = 2^3 \cdot (\sqrt[3]{6})^3 = 8 \cdot 6 = 48$$
7. $$\frac{6}{(3\sqrt{2})^2} = \frac{6}{3^2 \cdot (\sqrt{2})^2} = \frac{6}{9 \cdot 2} = \frac{6}{18} = \frac{1}{3}$$
8. $$-3\sqrt[3]{(-6)^3} = -3 \cdot (-6) = 18$$
9. $$\sqrt[4]{81} \cdot \sqrt[3]{8} = 3 \cdot 2 = 6$$
10. $$\sqrt[4]{1} \cdot \sqrt[3]{-0,125} = 1 \cdot (-0,5) = -0,5$$
11. $$\sqrt{27} \cdot \sqrt{9} = \sqrt{27 \cdot 9} = \sqrt{243} = \sqrt{81 \cdot 3} = 9\sqrt{3}$$
12. $$\sqrt[4]{9} \cdot \sqrt[4]{18} \cdot \sqrt[4]{8} = \sqrt[4]{9 \cdot 18 \cdot 8} = \sqrt[4]{9 \cdot 144} = \sqrt[4]{9 \cdot 9 \cdot 16} = \sqrt[4]{81 \cdot 16} = 3 \cdot 2 = 6$$
13. $$\frac{\sqrt[3]{500}}{5\sqrt[3]{4}} = \frac{\sqrt[3]{125 \cdot 4}}{5\sqrt[3]{4}} = \frac{5\sqrt[3]{4}}{5\sqrt[3]{4}} = 1$$