Преобразование выражений, содержащих степени. Задача 24math100admin44242025-03-26T20:27:33+03:00
Задача 24. Найдите значение выражения: \(\dfrac{{{{\left( {5{a^2}} \right)}^3} \cdot {{\left( {7b} \right)}^2}}}{{{{\left( {35{a^3}b} \right)}^2}}} + \dfrac{{9{{\left( {{m^4}} \right)}^3} + 7{{\left( {{m^3}} \right)}^4}}}{{{{\left( {2{m^6}} \right)}^2}}}\)
Решение
\(\dfrac{{{{\left( {5{a^2}} \right)}^3} \cdot {{\left( {7b} \right)}^2}}}{{{{\left( {35{a^3}b} \right)}^2}}} + \dfrac{{9{{\left( {{m^4}} \right)}^3} + 7{{\left( {{m^3}} \right)}^4}}}{{{{\left( {2{m^6}} \right)}^2}}} = \dfrac{{{5^3} \cdot {{\left( {{a^2}} \right)}^3} \cdot {7^2} \cdot {b^2}}}{{{{35}^2} \cdot {{\left( {{a^3}} \right)}^2} \cdot {b^2}}} + \dfrac{{9{m^{12}} + 7{m^{12}}}}{{{2^2} \cdot {{\left( {{m^6}} \right)}^2}}} = \)
\( = \dfrac{{{5^3} \cdot {7^2} \cdot {a^6}}}{{{5^2} \cdot {7^2} \cdot {a^6}}} + \dfrac{{16{m^{12}}}}{{4{m^{12}}}} = 5 + 4 = 9.\)
Ответ: 9.