Свойства степеней

$$49^{1/3} \cdot 49^{1/6} = 49^{\frac{1}{3}+\frac{1}{6}} = 49^{\frac{1}{2}} = \sqrt{49} = 7$$

$$5^{(3\sqrt{7}-1)+(1-\sqrt{7})-(2\sqrt{7}-1)} = 5^{3\sqrt{7}-\sqrt{7}-2\sqrt{7}+1} = 5^{1} = 5$$

Используем свойства степеней:

$$2^{3\sqrt{7}-1} \cdot (2^3)^{1-\sqrt{7}} = 2^{3\sqrt{7}-1} \cdot 2^{3-3\sqrt{7}} = 2^{(3\sqrt{7}-1)+(3-3\sqrt{7})} = 2^{2} = 4$$

$$\frac{(2^{-1})^{\sqrt{10}-1}}{2^{-\sqrt{10}}} = \frac{2^{-\sqrt{10}+1}}{2^{-\sqrt{10}}} = 2^{(-\sqrt{10}+1)-(-\sqrt{10})} = 2^{1} = 2$$

$$\frac{b^{3\sqrt{2}+2}}{b^{3\sqrt{2}}} = b^{(3\sqrt{2}+2)-3\sqrt{2}} = b^{2} = 6^2 = 36$$