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) \({(0,1)^{21}}:{( – 0,01)^{10}}\).
Ta thực hiện tính các phép tính theo quy tắc: nhân, chia trước; cộng, trừ sau.
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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) \(\begin{array}{l}{(0,1)^{21}}:{( – 0,01)^{10}} = {\left( {\frac{1}{{10}}} \right)^{21}}:{\left( {\frac{{ – 1}}{{100}}} \right)^{10}} = \frac{1}{{{{10}^{21}}}}:\frac{{{{( – 1)}^{10}}}}{{{{100}^{10}}}}\\{\rm{ }} = \frac{1}{{{{10}^{21}}}}{.100^{10}} = \frac{1}{{{{10}^{21}}}}{.10^{{2^{10}}}} = \frac{1}{{{{10}^{21}}}}{.10^{20}} = \frac{1}{{10}}\end{array}\).