Đề bài

Tính giá trị của mỗi biểu thức sau: a) \(1\frac{3}{4}.\frac{{ - 16}}{7}\);                                              b) \(12:\frac{{ - 6}}{5} + \frac{1}{5}\); c) \(\frac{2}{9} + \frac{1}{3}:\left( {\frac{{ - 3}}{2}} \right) + \frac{1}{2}.\left( { - 0,5} \right)\);                                                          d) \({(0,1)^{21}}:{( - 0,01)^{10}}\).

Lời giải chi tiết

a) \(1\frac{3}{4}.\frac{{ - 16}}{7} = \frac{7}{4}.\frac{{ - 16}}{7} = \frac{{ - 16}}{4} =  - 4\);                       b) \(12:\frac{{ - 6}}{5} + \frac{1}{5} = 12.\frac{5}{{ - 6}} + \frac{1}{5} =  - 10 + \frac{1}{5} = \frac{{ - 50}}{5} + \frac{1}{5} = \frac{{ - 49}}{5}\);c) \(\frac{2}{9} + \frac{1}{3}:\left( {\frac{{ - 3}}{2}} \right) + \frac{1}{2}.\left( { - 0,5} \right) = \;\frac{2}{9} + \frac{1}{3}.\left( {\frac{2}{{ - 3}}} \right) + \frac{1}{2}.\left( {\frac{{ - 1}}{2}} \right) = \frac{2}{9} + \frac{{ - 2}}{9} + \frac{{ - 1}}{4} = \frac{{ - 1}}{4}\;\);                                d) \(\begin{array}{l}{(0,1)^{21}}:{( - 0,01)^{10}} = {\left( {\frac{1}{{10}}} \right)^{21}}:{\left( {\frac{{ - 1}}{{100}}} \right)^{10}} = \frac{1}{{{{10}^{21}}}}:\frac{{{{( - 1)}^{10}}}}{{{{100}^{10}}}}\\{\rm{         }} = \frac{1}{{{{10}^{21}}}}{.100^{10}} = \frac{1}{{{{10}^{21}}}}{.10^{{2^{10}}}} = \frac{1}{{{{10}^{21}}}}{.10^{20}} = \frac{1}{{10}}\end{array}\).