293. Вычислить: 1) (1/16)^-0,75 + 10000^0,25 - (7 19/32)^1/5;

1) Переведем степени в дроби: $0,75 = \frac{3}{4}$, $0,25 = \frac{1}{4}$. $\left(\frac{1}{16}\right)^{-\frac{3}{4}} = (16)^{\frac{3}{4}} = (2^4)^{\frac{3}{4}} = 2^3 = 8$. $10000^{\frac{1}{4}} = (10^4)^{\frac{1}{4}} = 10^1 = 10$. $7\frac{19}{32} = \frac{7 \cdot 32 + 19}{32} = \frac{224 + 19}{32} = \frac{243}{32} = \left(\frac{3}{2}\right)^5$. $\left(\frac{243}{32}\right)^{\frac{1}{5}} = \frac{3}{2} = 1,5$. Итог: $8 + 10 - 1,5 = 16,5$. 2) $(0,001)^{-\frac{1}{3}} = (10^{-3})^{-\frac{1}{3}} = 10^1 = 10$. $2^{-2} \cdot 64^{\frac{2}{3}} = \frac{1}{2^2} \cdot (2^6)^{\frac{2}{3}} = \frac{1}{4} \cdot 2^4 = \frac{16}{4} = 4$. $8^{-\frac{1}{3}} = (2^3)^{-\frac{1}{3}} = 2^{-1} = 0,5$. Итог: $10 - 4 - 0,5 = 5,5$. 3) $27^{\frac{2}{3}} = (3^3)^{\frac{2}{3}} = 3^2 = 9$. $(-2)^{-2} = \frac{1}{(-2)^2} = \frac{1}{4} = 0,25$. $3\frac{3}{8} = \frac{27}{8} = \left(\frac{3}{2}\right)^3$. $\left(\frac{27}{8}\right)^{\frac{1}{3}} = \frac{3}{2} = 1,5$. Итог: $9 - 0,25 + 1,5 = 10,25$. 4) $(-0,5)^{-4} = \left(-\frac{1}{2}\right)^{-4} = (-2)^4 = 16$. $2\frac{1}{4} = \frac{9}{4} = \left(\frac{3}{2}\right)^2$. $\left(\frac{9}{4}\right)^{-\frac{3}{2}} = \left(\left(\frac{3}{2}\right)^2\right)^{-\frac{3}{2}} = \left(\frac{3}{2}\right)^{-3} = \left(\frac{2}{3}\right)^3 = \frac{8}{27}$. Итог: $16 - 625 - \frac{8}{27} = -609 - \frac{8}{27} = -609\frac{8}{27}$.