Задача 4. Вычислите    \({\left( {3\dfrac{3}{8}} \right)^{\frac{2}{3}}} + {\left( {\dfrac{1}{8}} \right)^{\frac{2}{3}}}\) 

Ответ

ОТВЕТ: 2,5.

Решение

\({\left( {3\dfrac{3}{8}} \right)^{\frac{2}{3}}} + {\left( {\dfrac{1}{8}} \right)^{\frac{2}{3}}} = {\left( {\dfrac{{27}}{8}} \right)^{\frac{2}{3}}} + {\left( {{{\left( {\dfrac{1}{2}} \right)}^3}} \right)^{\frac{2}{3}}} = {\left( {{{\left( {\dfrac{3}{2}} \right)}^3}} \right)^{\frac{2}{3}}} + {\left( {\dfrac{1}{2}} \right)^{3 \cdot \frac{2}{3}}} = \)

\( = {\left( {\dfrac{3}{2}} \right)^{3 \cdot \frac{2}{3}}} + {\left( {\dfrac{1}{2}} \right)^2} = {\left( {\dfrac{3}{2}} \right)^2} + \dfrac{1}{4} = \dfrac{9}{4} + \dfrac{1}{4} = \dfrac{{10}}{4} = 2,5.\)

Ответ:  2,5.