Вычисления и преобразования

$$\dfrac{a^{7,4}}{a^{8,4}} = a^{7,4-8,4} = a^{-1} = \dfrac{1}{a} = \dfrac{1}{0,4} = 2,5$$

$$\frac{a^{1/9} \cdot a^{1/18}}{a \cdot a^{1/6}} = \frac{a^{\frac{1}{9}+\frac{1}{18}}}{a^{1+\frac{1}{6}}} = \frac{a^{\frac{1}{6}}}{a^{\frac{7}{6}}} = a^{\frac{1}{6}-\frac{7}{6}} = a^{-1} = \dfrac{1}{a} = \dfrac{1}{1,25} = 0,8$$

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

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

Используем свойства степеней:

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