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a)\({\left( { - 2} \right)^2}.{\left( { - 2} \right)^3} = {\left( { - 2} \right)^{2 + 3}} = {\left( { - 2} \right)^5}\);
b)\({\left( { - 0,25} \right)^7}:{\left( { - 0,25} \right)^5} = {\left( { - 0,25} \right)^{7 - 5}} = {\left( { - 0,25} \right)^2} = {\left( {0,25} \right)^2}\);
c)\({\left( {\frac{3}{4}} \right)^4}.{\left( {\frac{3}{4}} \right)^3} = {\left( {\frac{3}{4}} \right)^{4 + 3}} = {\left( {\frac{3}{4}} \right)^7}.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \({\left( {\frac{8}{9}} \right)^3} \cdot \frac{4}{3} \cdot \frac{2}{3} = {\left( {\frac{8}{9}} \right)^3}.\frac{8}{9} = {\left( {\frac{8}{9}} \right)^{3+1}}={\left( {\frac{8}{9}} \right)^4}\)
b) \({\left( {\frac{1}{4}} \right)^7} \cdot 0,25 = {\left( {0,25} \right)^7}.0,25 ={\left( {0,25} \right)^{7+1}}= {\left( {0,25} \right)^8}\)
c) \({( - 0,125)^6}:\frac{{ - 1}}{8} = {\left( {\frac{{ - 1}}{8}} \right)^6}:\frac{{ - 1}}{8} = {\left( {\frac{{ - 1}}{8}} \right)^{6-1}}= {\left( {\frac{{ - 1}}{8}} \right)^5}\)
d) \({\left[ {{{\left( {\frac{{ - 3}}{2}} \right)}^3}} \right]^2} = {\left( {\frac{{ - 3}}{2}} \right)^{3.2}} = {\left( {\frac{{ - 3}}{2}} \right)^6}\)
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\(S=\frac{3}{4}-0,25\left[\frac{7}{3}+\left(-\frac{9}{2}\right)\right]-\frac{5}{6}\)
\(\Rightarrow S=\frac{3}{4}-0,25.\frac{13}{6}-\frac{5}{6}\)
\(\Rightarrow S=\frac{3}{4}-\frac{1}{4}.\frac{13}{6}-\frac{5}{6}\)
\(\Rightarrow S=\frac{18}{24}-\frac{13}{24}-\frac{20}{24}\)
\(\Rightarrow S=\frac{18-13-20}{24}=\frac{-15}{24}\)
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\(\begin{array}{l}\frac{7}{6}.3\frac{1}{4} + \frac{7}{6}.( - 0,25)\\ = \frac{7}{6}.\frac{{13}}{4} + \frac{7}{6}.\frac{{ - 25}}{{100}}\\ = \frac{7}{6}.\frac{{13}}{4} + \frac{7}{6}.\frac{{ - 1}}{4}\\ = \frac{7}{6}.[\left( {\frac{{13}}{4} + ( - \frac{1}{4})} \right)]\\ = \frac{7}{6}.\frac{{12}}{4}\\ = \frac{7}{6}.3\\ = \frac{7}{2}\end{array}\)
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\(\left(-2\right)^3.\left(\frac{3}{4}-0,25\right):\left(2\frac{1}{4}-1\frac{1}{6}\right)\)
\(=-8.\left(\frac{3}{4}-\frac{1}{4}\right):\left(\frac{9}{4}-\frac{7}{6}\right)\)
\(=-8.\frac{1}{2}:\left(\frac{54}{24}-\frac{28}{24}\right)\)
\(=-4:\frac{13}{12}\)
\(=-4.\frac{13}{12}\)
\(=\frac{-13}{3}\)
\((-2)^3\cdot(\frac{3}{4}-0,25):(2\frac{1}{4}-1\frac{1}{6})\)
\(=-8\cdot(0,75-0,25):(\frac{9}{4}-\frac{7}{6})\)
\(=-8\cdot0,5:\frac{13}{12}\)
\(=-8\cdot0,5\cdot\frac{12}{13}\)
\(=-4\cdot\frac{12}{13}=-\frac{48}{13}=-3\frac{9}{13}\)
\(=2\frac{4}{13}\)
\(\text{Bài toán này .... tính mất công }:)\text{ Bạn dùng máy tính thử kiểm tra có đúng không ?}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\left(0,25\right)^{-1}.\left(\frac{1}{4}\right)^{-2}.\left(\frac{4}{3}\right)^2.\left(\frac{5}{4}\right)^{-1}.\left(\frac{2}{3}\right)^{-3}\)
\(\Rightarrow A=4^1.4^2.\frac{16}{9}.\frac{4}{5}\frac{27}{8}\)
\(\Rightarrow A=\frac{64}{1}.\frac{16}{9}.\frac{4}{5}.\frac{27}{8}\)
\(\Rightarrow A=\frac{1536}{5}\)
Vậy \(A=\frac{1536}{5}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
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\(=\frac{1}{4}:\frac{1}{2}-\frac{3}{4}=\frac{1}{2}-\frac{3}{4}=-\frac{1}{4}\)