\[{\text{Вычислить: }}\left( {\sqrt[3]{{128}} + \sqrt[3]{{\frac{1}{4}}}} \right):\sqrt[3]{2}.\]
\[\sqrt[n]{{{a^m}}} = {a^{\frac{m}{n}}}\]
\[\begin{array}{l}\left( {\sqrt[3]{{128}} + \sqrt[3]{{\frac{1}{4}}}} \right):\sqrt[3]{2} = \left( {\sqrt[3]{{{2^7}}} + \sqrt[3]{{{2^{ - 2}}}}} \right):{2^{\frac{1}{3}}} = \left( {{2^{\frac{7}{3}}} + {2^{ - \frac{2}{3}}}} \right):{2^{\frac{1}{3}}} = \\{2^{\frac{7}{3} - \frac{1}{3}}} + {2^{ - \frac{2}{3} - \frac{1}{3}}} = {2^{\frac{6}{3}}} + {2^{ - 1}} = {2^2} + \frac{1}{2} = 4 + 0,5 = 4,5\end{array}\]
\[4,5\]
