1188. a) $$\sqrt[4]{2^3\sqrt{2}m^4n^8}$$;

a) $$\sqrt[4]{2^3\sqrt{2}m^4n^8}$$

$$\sqrt[4]{2^3\sqrt{2}m^4n^8} = \sqrt[4]{2^3 \cdot 2^{\frac{1}{2}}m^4n^8} = \sqrt[4]{2^{\frac{6}{2}} \cdot 2^{\frac{1}{2}}m^4n^8} = \sqrt[4]{2^{\frac{7}{2}}m^4n^8} = 2^{\frac{7}{2*4}}mn^{\frac{8}{4}} = 2^{\frac{7}{8}}mn^2 = \sqrt[8]{2^7}mn^2 = mn^2\sqrt[8]{128}$$

Ответ: $$mn^2\sqrt[8]{128}$$