Giải Bài 6 trang 15 sách bài tập toán 7 tập 1 - Chân trời sáng tạo

Đề bài

Tính

a) \({\left( {\dfrac{2}{5} - \dfrac{1}{3}} \right)^2}\)

b) \({\left( {1\dfrac{1}{2} - 1,25} \right)^3}\)

c) \({\left( {\dfrac{1}{2} + \dfrac{1}{3}} \right)^2}:{\left( {1\dfrac{1}{2}} \right)^2}\)

d) \(2:{\left( {\dfrac{1}{2} - \dfrac{2}{3}} \right)^3}\)

Lời giải chi tiết

\(\begin{array}{l}a){\left( {\dfrac{2}{5} - \dfrac{1}{3}} \right)^2} = {\left( {\dfrac{6}{{15}} - \dfrac{5}{{15}}} \right)^2} = {\left( {\dfrac{1}{{15}}} \right)^2} = \dfrac{{1.1}}{{15.15}} = \dfrac{1}{{225}}\\b){\left( {1\dfrac{1}{2} - 1,25} \right)^3} = {\left( {\dfrac{3}{2} - \dfrac{5}{4}} \right)^3} = {\left( {\dfrac{1}{4}} \right)^3} = \dfrac{1}{{64}}\\c){\left( {\dfrac{1}{2} + \dfrac{1}{3}} \right)^2}:{\left( {1\dfrac{1}{2}} \right)^2} = {\left( {\dfrac{5}{6}} \right)^2}:{\left( {\dfrac{3}{2}} \right)^2} = \dfrac{{25}}{{36}}.\dfrac{4}{9} = \dfrac{{25}}{{81}}\\d)2:{\left( {\dfrac{1}{2} - \dfrac{2}{3}} \right)^3} = 2:{\left( {\dfrac{{ - 1}}{6}} \right)^3} = 2.\dfrac{{6.6.6}}{{( - 1).( - 1).( - 1)}} = 2.{( - 6)^3} = 2.( - 216) =  - 432\end{array}\)