1191. a) $$^3\sqrt{a^3\sqrt[3]{a^3}\sqrt{a}} : \sqrt[14]{a^{27}}$$.

1191. a) $$^3\sqrt{a^3\sqrt[3]{a^3}\sqrt{a}} : \sqrt[14]{a^{27}}$$.

$$^3\sqrt{a^3\sqrt[3]{a^3}\sqrt{a}} : \sqrt[14]{a^{27}} = \sqrt[3]{a^3\cdot a^{\frac{3}{3}}\cdot a^{\frac{1}{2}}} : \sqrt[14]{a^{27}} = \sqrt[3]{a^3\cdot a\cdot a^{\frac{1}{2}}} : \sqrt[14]{a^{27}} = \sqrt[3]{a^{\frac{6}{2}}\cdot a^{\frac{2}{2}}\cdot a^{\frac{1}{2}}} : \sqrt[14]{a^{27}} = \sqrt[3]{a^{\frac{9}{2}}} : \sqrt[14]{a^{27}} = a^{\frac{9}{2*3}} : a^{\frac{27}{14}} = a^{\frac{3}{2}} : a^{\frac{27}{14}} = a^{\frac{3}{2} - \frac{27}{14}} = a^{\frac{21-27}{14}} = a^{\frac{-6}{14}} = a^{\frac{-3}{7}} = \frac{1}{a^{\frac{3}{7}}} = \frac{1}{\sqrt[7]{a^3}}$$

Ответ: $$\frac{1}{\sqrt[7]{a^3}}$$