The user wants me to solve the mathematical expressions from the image.

Решение:

1. \( \sqrt{400} \cdot 2 - \frac{1}{3}\sqrt{81} = 2 \cdot 20 - \frac{1}{3} \cdot 9 = 40 - 3 = 37 \)
2. \( 5\sqrt{64} - \sqrt{5^2 + 12^2} = 5 \cdot 8 - \sqrt{25 + 144} = 40 - \sqrt{169} = 40 - 13 = 27 \)
3. \( \sqrt{\frac{9}{16} \cdot \frac{49}{169}} - 3\sqrt{0.49} + 2.6 = \sqrt{\frac{3^2}{4^2} \cdot \frac{7^2}{13^2}} - 3 \cdot 0.7 + 2.6 = \frac{3 \cdot 7}{4 \cdot 13} - 2.1 + 2.6 = \frac{21}{52} + 0.5 = \frac{21}{52} + \frac{26}{52} = \frac{47}{52} \)
4. \( \frac{1}{8}\sqrt{0.64} - 1 = \frac{1}{8} \cdot 0.8 - 1 = 0.1 - 1 = -0.9 \)