Вычисления и преобразования

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

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

$$\frac{(6 \cdot 7)^{\sqrt{3}}}{42^{\sqrt{3}-1}} = \frac{42^{\sqrt{3}}}{42^{\sqrt{3}-1}} = 42^{\sqrt{3}-(\sqrt{3}-1)} = 42^{1} = 42$$

$$\frac{b^{\sqrt{3} \cdot 2\sqrt{3}}}{b^4} = \frac{b^{6}}{b^4} = b^{2} = 5^2 = 25$$

Воспользуемся формулами приведения:

$$\frac{5\sin98^\circ}{\sin49^{\circ} \cdot \sin(90 - 49)^{\circ}} = \frac{5\sin98^\circ}{\sin49^{\circ} \cdot \cos49^{\circ}} = \frac{5\sin98^\circ}{\frac{1}{2}\cdot\sin98^\circ} = 5\cdot2 = 10$$