Преобразование выражений, содержащих степени. Задача 9math100admin44242025-03-26T20:03:41+03:00
Задача 9. Вычислите \({4^{\frac{3}{5}}} \cdot {16^{\frac{1}{5}}}-\dfrac{{{2^{2,2}} \cdot {3^{5,2}}}}{{{6^{4,2}}}}\)
Решение
\({4^{\frac{3}{5}}} \cdot {16^{\frac{1}{5}}}-\dfrac{{{2^{2,2}} \cdot {3^{5,2}}}}{{{6^{4,2}}}} = {4^{\frac{3}{5}}} \cdot {\left( {{4^2}} \right)^{\frac{1}{5}}}-\dfrac{{{2^{2,2}} \cdot {3^{5,2}}}}{{{{\left( {2 \cdot 3} \right)}^{4,2}}}} = {4^{\frac{3}{5}}} \cdot {4^{\frac{2}{5}}}-\dfrac{{{2^{2,2}} \cdot {3^{5,2}}}}{{{2^{4,2}} \cdot {3^{4,2}}}} = \)
\( = {4^{\frac{3}{5} + \frac{2}{5}}}-\dfrac{{{3^{5,2-4,2}}}}{{{2^{4,2-2,2}}}} = {4^1}-\dfrac{{{3^1}}}{{{2^2}}} = 4-\dfrac{3}{4} = 3,25.\)
Ответ: 3,25.