10. Тип 10 № 11155 Найдите значение выражения $$\left(\frac{x^2}{2a^3}\right)^3 \cdot \left(\frac{4a^4}{x^5}\right)^2$$ при $$a = -\frac{1}{13}$$ и $$x = -0.31$$.

$$\left(\frac{x^2}{2a^3}\right)^3 \cdot \left(\frac{4a^4}{x^5}\right)^2 = \frac{x^6}{8a^9} \cdot \frac{16a^8}{x^{10}} = \frac{2}{1} \cdot \frac{2a^8x^6}{a^9x^{10}}= \frac{2}{1} \cdot \frac{2}{1} \cdot \frac{2}{1} \cdot \frac{16}{8} \cdot \frac{a^8x^6}{a^9x^{10}} = 2\frac{a^8x^6}{a^9x^{10}} = \frac{2}{ax^4}$$ $$a = -\frac{1}{13}$$, $$x = -0.31 = -\frac{31}{100}$$ $$\frac{2}{ax^4} = \frac{2}{(-\frac{1}{13})(-\frac{31}{100})^4} = \frac{2}{(-\frac{1}{13})(\frac{31^4}{100^4})} = \frac{2}{(-\frac{1}{13})(\frac{923521}{100000000})} = \frac{2}{-\frac{923521}{1300000000}} = 2 \cdot -\frac{1300000000}{923521} = -\frac{2600000000}{923521} \approx -2815.3$$