Giải bài 1.23 trang 19

Đề bài

Tính:

a) ${\left(1+\frac{1}{2}-\frac{1}{4}\right)}^2.\left(2+\frac{3}{7}\right)$

b) $4:{\left(\frac{1}{2}-\frac{1}{3}\right)}^3$

Lời giải chi tiết

a)

$\begin{array}{c}{\left(1+\frac{1}{2}-\frac{1}{4}\right)}^2.\left(2+\frac{3}{7}\right)\\ ={\left(\frac{4}{4}+\frac{2}{4}-\frac{1}{4}\right)}^2.\left(\frac{14}{7}+\frac{3}{7}\right)\\ ={\left(\frac{5}{4}\right)}^2.\frac{17}{7}\\ =\frac{25}{16}.\frac{17}{7}\\ =\frac{425}{112}\end{array}$

b)

$\begin{array}{c}4:{\left(\frac{1}{2}-\frac{1}{3}\right)}^3\\ =4:{\left(\frac{3}{6}-\frac{2}{6}\right)}^3\\ =4:{\left(\frac{1}{6}\right)}^3\\ =4:\frac{1}{216}\\ =4.216\\ =864\end{array}$