Преобразование выражений, содержащих степени. Задача 4math100admin44242025-03-26T19:58:04+03:00
Задача 4. Вычислите \({\left( {3\dfrac{3}{8}} \right)^{\frac{2}{3}}} + {\left( {\dfrac{1}{8}} \right)^{\frac{2}{3}}}\)
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.