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a)
\(\begin{array}{l}{\left( {\frac{{ - 1}}{2}} \right)^5} = \frac{{{{\left( { - 1} \right)}^5}}}{{{2^5}}} = \frac{{ - 1}}{{32}};\\{\left( {\frac{{ - 2}}{3}} \right)^4} = \frac{{{{\left( { - 2} \right)}^4}}}{{{3^4}}} = \frac{{16}}{{81}};\\{\left( { - 2\frac{1}{4}} \right)^3} = {\left( {\frac{{ - 9}}{4}} \right)^3} = \frac{{{{\left( { - 9} \right)}^3}}}{{{4^3}}} = \frac{{-729}}{{64}};\\{\left( { - 0,3} \right)^5} = {\left( {\frac{{ - 3}}{{10}}} \right)^5} = \frac{{ - 243}}{{100000}};\\{\left( { - 25,7} \right)^0} = 1\end{array}\)
b)
\(\begin{array}{l}{\left( { - \frac{1}{3}} \right)^2} = \frac{1}{9};\\{\left( { - \frac{1}{3}} \right)^3} = \frac{{ - 1}}{{27}};\\{\left( { - \frac{1}{3}} \right)^4} = \frac{1}{{81}};\\{\left( { - \frac{1}{3}} \right)^5} = \frac{{ - 1}}{{243}}.\end{array}\)
Nhận xét:
+ Luỹ thừa của một số hữu tỉ âm với số mũ chẵn là một số hữu tỉ dương.
+ Luỹ thừa của một số hữu tỉ âm với số mũ lẻ là một số hữu tỉ âm.
A = (1 - 2/3 + 4/3) - (4/5 - 1) + (7/5 + 2)
A= (3/3 - 2/3 + 4/3) - (4/5 - 5/5) + (7/5 + 10/5)
A= 5/3 + 1/5 + 17/5
A= 5/3 +18/5
A= 25/15 + 54/15
A= 79/15
B= (-3 + 3/4 - 1/3 ) : (5 + 2/5 - 2/3)
B= (-36/12 + 9/12 - 4/12) : (75/15 + 6/15 - 10/15)
B= -31/12 : 71/15
B= -155/284
C= (3/5 - 4/5 ) . (2/7 - 3/14) - (5/9 - 7/27) . (1 - 3/5) + (1 - 11/12) . (1-11/12)
C= -1/5 . 1/14 - 8/27 . 2/5 + 1/12 . 1/12
C=-1/70 - 16/135 + 1/144
C=-216/15120 - 1792/15120 + 105/15120
C=-1903/15120
\(a,\left[\left(-\frac{1}{2}\right)^3-\left(\frac{3}{4}\right)^3.\left(-2\right)^2\right]:\left[2.\left(-1\right)^5+\left(\frac{3}{4}\right)^2-\frac{3}{8}\right]\)
\(=\left[\left(-\frac{1}{8}\right)-\frac{27}{64}.4\right]:\left[2.\left(-1\right)+\frac{9}{16}-\frac{3}{8}\right]\)
\(=\left[\left(-\frac{1}{8}-\frac{27}{16}\right)\right]:\left[-2+\frac{9}{16}-\frac{3}{8}\right]\)
\(=\frac{-2-27}{16}:\frac{-32+9-6}{16}\)
\(=-\frac{29}{16}:\frac{-29}{16}=1\)
\(b,\left[\left(\frac{4}{3}\right)^{-2}\left(\frac{3}{2}\right)^4\right]:\left(\frac{3}{2}\right)^6\)
\(=\left(\frac{9}{16}.\frac{81}{16}\right):\frac{729}{64}\)
\(=\frac{729}{64}:\frac{729}{64}=1\)
\(\left(\frac{4}{9}+\frac{1}{3}\right)^2=\left(\frac{4}{9}+\frac{3}{9}\right)^2=\left(\frac{7}{9}\right)^2=\frac{49}{81}\)
\(\left(\frac{1}{2}-\frac{3}{5}\right)^3=\left(\frac{5}{10}-\frac{6}{10}\right)^3=\left(\frac{-1}{10}\right)^3=\frac{-1}{1000}\)
\(\left(\frac{-1}{5}\right)^5.\left(\frac{-6}{5}\right)^4=\frac{-5}{3125}.\frac{1296}{625}=\frac{-1296}{390625}\)
\(\left(\frac{3}{4}\right)^3:\left(\frac{3}{4}\right)^2:\left(-\frac{2}{5}\right)^3=\frac{3}{4}:\frac{-8}{125}=\frac{3}{4}.\frac{-125}{8}=\frac{-375}{32}\)
.
\(A=\left(\frac{3}{4}\right)^{-4}.\left(\frac{-2}{3}\right)^{-3}\)
\(A=\frac{256}{81}.\frac{-27}{8}\)
\(A=\frac{729}{64}\)
\(B=\left(4^3\right)^{-2}.a^{2015}\)
\(B=64^{-2}.a^{2015}\)
\(B=\frac{1}{4096}.a^{2015}\)
\(C=\left[\left(\frac{-1}{3}\right).\frac{2}{5}.\left(\frac{-3}{4}\right)\right]^3\)
\(C=\left[\frac{1}{10}\right]^3\)
\(C=\frac{1}{1000}\)
A =\(-\frac{32}{3}\)
B = \(\frac{1}{4096}.a^{2015}\)
C =\(\frac{1}{1000}\)