Преобразование выражений, содержащих степени. Задача 11math100admin44242025-03-26T20:10:15+03:00
Задача 11. Вычислите \({6^{2,3}} \cdot {3^{-0,3}}:{2^{2,3}} + \dfrac{{{{\left( {{5^{\frac{4}{7}}} \cdot {9^{\frac{2}{3}}}} \right)}^{21}}}}{{{{45}^{12}}}}\)
Решение
\({6^{2,3}} \cdot {3^{-0,3}}:{2^{2,3}} + \dfrac{{{{\left( {{5^{\frac{4}{7}}} \cdot {9^{\frac{2}{3}}}} \right)}^{21}}}}{{{{45}^{12}}}} = \dfrac{{{{\left( {2 \cdot 3} \right)}^{2,3}} \cdot {3^{-0,3}}}}{{{2^{2,3}}}} + \dfrac{{{{\left( {{5^{\frac{4}{7}}}} \right)}^{21}} \cdot {{\left( {{9^{\frac{2}{3}}}} \right)}^{21}}}}{{{{\left( {5 \cdot 9} \right)}^{12}}}} = \)
\( = \dfrac{{{2^{2,3}} \cdot {3^{2,3}} \cdot {3^{-0,3}}}}{{{2^{2,3}}}} + \dfrac{{{5^{\frac{4}{7} \cdot 21}} \cdot {9^{\frac{2}{3} \cdot 21}}}}{{{5^{12}} \cdot {9^{12}}}} = {3^{2,3-0,3}} + \dfrac{{{5^{12}} \cdot {9^{14}}}}{{{5^{12}} \cdot {9^{12}}}} = {3^2} + {9^2} = 9 + 81 = 90.\)
Ответ: 90.