37.19. a) $$(a^{0.4})^{\frac{1}{2}} \cdot a^{0.8}$$; б) $$\sqrt[10]{c} \cdot (c^{-1.2})^{\frac{3}{4}}$$; в) $$(x^{\frac{3}{4}})^{\frac{5}{4}} \cdot (\sqrt[4]{x})^{\frac{17}{4}}$$; г) $$(b^{0.8})^{-\frac{3}{4}} \cdot (b^{\frac{2}{5}})^{-1.5}$$.

a) $$(a^{0.4})^{\frac{1}{2}} \cdot a^{0.8} = a^{0.4 \cdot \frac{1}{2}} \cdot a^{0.8} = a^{0.2} \cdot a^{0.8} = a^{0.2 + 0.8} = a^1 = a$$. б) $$\sqrt[10]{c} \cdot (c^{-1.2})^{\frac{3}{4}} = c^{\frac{1}{10}} \cdot c^{-1.2 \cdot \frac{3}{4}} = c^{\frac{1}{10}} \cdot c^{-\frac{12}{10} \cdot \frac{3}{4}} = c^{\frac{1}{10}} \cdot c^{-\frac{36}{40}} = c^{\frac{1}{10}} \cdot c^{-\frac{9}{10}} = c^{\frac{1}{10} - \frac{9}{10}} = c^{-\frac{8}{10}} = c^{-\frac{4}{5}}$$. в) $$(x^{\frac{3}{4}})^{\frac{5}{4}} \cdot (\sqrt[4]{x})^{\frac{17}{4}} = x^{\frac{3}{4} \cdot \frac{5}{4}} \cdot (x^{\frac{1}{4}})^{\frac{17}{4}} = x^{\frac{15}{16}} \cdot x^{\frac{1}{4} \cdot \frac{17}{4}} = x^{\frac{15}{16}} \cdot x^{\frac{17}{16}} = x^{\frac{15}{16} + \frac{17}{16}} = x^{\frac{32}{16}} = x^2$$. г) $$(b^{0.8})^{-\frac{3}{4}} \cdot (b^{\frac{2}{5}})^{-1.5} = b^{0.8 \cdot (-\frac{3}{4})} \cdot b^{\frac{2}{5} \cdot (-1.5)} = b^{\frac{8}{10} \cdot (-\frac{3}{4})} \cdot b^{\frac{2}{5} \cdot (-\frac{3}{2})} = b^{-\frac{24}{40}} \cdot b^{-\frac{6}{10}} = b^{-\frac{3}{5}} \cdot b^{-\frac{3}{5}} = b^{-\frac{3}{5} - \frac{3}{5}} = b^{-\frac{6}{5}}$$. Ответ: а) $$a$$, б) $$c^{-\frac{4}{5}}$$, в) $$x^2$$, г) $$b^{-\frac{6}{5}}$$