\[\boxed{\text{257}\text{\ (257)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)} - 0,5\sqrt[10]{1024} = - 0,5 \cdot \sqrt[10]{2^{10}} =\]
\[= - 0,5 \cdot 2 = - 1;\]
\[\textbf{б)} - \frac{2}{3}\sqrt[7]{- 2187} =\]
\[= - \frac{2}{3} \cdot \sqrt[7]{( - 3)^{7}} =\]
\[= - \frac{2}{3} \cdot ( - 3) = 2;\]
\[\textbf{в)}\ 1,5\sqrt[9]{512} = 1,5\sqrt[9]{2^{9}} =\]
\[= 1,5 \cdot 2 = 3;\]
\[\textbf{г)}\ \sqrt[5]{7\frac{19}{32}} \cdot \sqrt{5\frac{4}{9}} = \sqrt[5]{\frac{243}{32}} \cdot \sqrt{\frac{49}{9}} =\]
\[= \sqrt[5]{\frac{3^{5}}{2^{5}}} \cdot \sqrt{\frac{49}{9}} = \frac{3}{2} \cdot \frac{7}{3} = \frac{7}{2};\]
\[\textbf{д)}\ \sqrt[3]{- 125} \cdot \sqrt[7]{{0,1}^{7}} = - 5 \cdot 0,1 =\]
\[= - 0,5;\]
\[\textbf{е)}\ \sqrt[4]{16^{- 2}} \cdot \sqrt[3]{{0,125}^{3}} =\]
\[= \sqrt[4]{\frac{1}{4^{4}}} \cdot 0,125 = \frac{1}{4} \cdot \frac{1}{8} = \frac{1}{32}.\]