Bài 7 trang 21 toán lớp 7 tập 1 CTSTTính:a) $\left ( \frac{2}{5} + \frac{1}{2}\right )^{2}$b)...

a)
Cách 1:
$\left ( \frac{2}{5} + \frac{1}{2}\right )^{2}$ = $\left ( \frac{4}{10} + \frac{5}{10}\right )^{2}$ = $\left ( \frac{9}{10}\right )^{2}$ = $\frac{81}{100}$

Cách 2:
$\left ( \frac{2}{5} + \frac{1}{2}\right )^{2} = \left ( \frac{4+5}{10}\right )^{2} = \left ( \frac{9}{10}\right )^{2} = \frac{81}{100}$

b)
Cách 1:
$\left ( 0,75 + 1\frac{1}{2}\right )^{3}$ = $\left ( \frac{3}{4} + \frac{3}{2}\right )^{2}$ = $\left ( \frac{3}{4} + \frac{6}{4}\right )^{2}$ = $( \frac{9}{4} )^{2}$ = $\frac{81}{16}$

Cách 2:
$\left ( 0,75 + 1\frac{1}{2}\right )^{3} = \left ( \frac{3}{4} + \frac{3}{2}\right )^{3} = \left ( \frac{3}{4} + \frac{6}{4}\right )^{3} = (\frac{9}{4})^{3} = \frac{729}{64}$

c)
$\left ( \frac{3}{5} \right )^{15}$ : (0,36)^5 = $\left ( \frac{3}{5} \right )^{15}$ : $\left ( \frac{36}{100} \right )^5$ = $\left ( \frac{3}{5} \right )^{15}$ : $\left ( \frac{9}{25} \right )^5$ = $\left ( \frac{3}{5} \right )^{15}$ : $\left ( \frac{9^{5}}{25^{5}} \right )$ = $\left ( \frac{3}{5} \right )^{15}$ : $\frac{3}{5}$ = 1

d)
$\left ( 1 - \frac{1}{3}\right )^{8}$ : $\left ( \frac{4}{9} \right )^{3}$ = $\left ( \frac{2}{3}\right )^{8}$ : $\left ( \frac{4}{9} \right )^{3}$ = $\left ( \frac{2^{8}}{3^{8}}\right )$ : $\left ( \frac{4^{3}}{9^{3}} \right )$ = $\left ( \frac{2^{8} \cdot 9^{3}}{3^{8} \cdot 4^{3}} \right )$ = $\frac{27}{16}$

Như vậy:
a) $\left ( \frac{2}{5} + \frac{1}{2}\right )^{2}$ = $\frac{81}{100}$
b) $\left ( 0,75 + 1\frac{1}{2}\right )^{3}$ = $\frac{81}{16}$
c) $\left ( \frac{3}{5} \right )^{15}$ : (0,36)^5 = 1
d) $\left ( 1 - \frac{1}{3}\right )^{8}$ : $\left ( \frac{4}{9} \right )^{3}$ = $\frac{27}{16}$