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.

1+1=3 :)))

\(\text{Ta có: }Q=\left(\frac{3}{4}\right)+\left(\frac{3}{4}\right)^2+\left(\frac{3}{4}\right)^3+.....+\left(\frac{3}{4}\right)^{2016}\)

\(\Rightarrow\frac{3}{4}Q=\left(\frac{3}{4}\right)^2+\left(\frac{3}{4}\right)^3+\left(\frac{3}{4}\right)^4+......+\left(\frac{3}{4}\right)^{2017}\)

\(\Rightarrow Q-\frac{3}{4}Q=\frac{3}{4}-\left(\frac{3}{4}\right)^{2017}\)

\(\Rightarrow\frac{1}{4}Q=\frac{3}{4}-\left(\frac{3}{4}\right)^{2017}\)

\(\Rightarrow Q=\text{[}\frac{3}{4}-\left(\frac{3}{4}\right)^{2017}\text{]}.4\)

\(\Rightarrow Q=3-\)

\(a,\left[\left(-\frac{1}{2}\right)^3-\left(\frac{3}{4}\right)^3.\left(-2\right)^2\right]:\left[2.\left(-1\right)^5+\left(\frac{3}{4}\right)^2-\frac{3}{8}\right]\)

\(=\left[\left(-\frac{1}{8}\right)-\frac{27}{64}.4\right]:\left[2.\left(-1\right)+\frac{9}{16}-\frac{3}{8}\right]\)

\(=\left[\left(-\frac{1}{8}-\frac{27}{16}\right)\right]:\left[-2+\frac{9}{16}-\frac{3}{8}\right]\)

\(=\frac{-2-27}{16}:\frac{-32+9-6}{16}\)

\(=-\frac{29}{16}:\frac{-29}{16}=1\)

\(b,\left[\left(\frac{4}{3}\right)^{-2}\left(\frac{3}{2}\right)^4\right]:\left(\frac{3}{2}\right)^6\)

\(=\left(\frac{9}{16}.\frac{81}{16}\right):\frac{729}{64}\)

\(=\frac{729}{64}:\frac{729}{64}=1\)

\(\left[\left(\frac{4}{3}\right)^{-2}.\left(\frac{3}{4}\right)^3\right]:\left(-\frac{2}{3}\right)^{-3}\)

\(=\frac{9}{16}.\frac{27}{64}:\left(-\frac{27}{8}\right)\)

\(=-\frac{9}{128}\)

[(3/4)^-2.(3/4)³]:(-2/3)^-3

=[16/9.3/64]:9/4

=1/12:9/4

=1/27

\(\left[\frac{9}{16}.\frac{27}{64}\right]:\frac{-27}{8}\)

\(\frac{243}{1024}:\frac{-27}{8}=\frac{-9}{128}\)

=> A = \(\frac{\frac{3}{64}+\frac{5}{64}-\frac{5}{2}}{\frac{-5}{64}+\frac{2}{9}-\frac{5}{6}}\)= \(\frac{\frac{1}{8}-\frac{5}{2}}{\frac{83}{576}-\frac{5}{6}}\)= \(\frac{\frac{-19}{8}}{\frac{-397}{576}}\)= \(\frac{1368}{397}\)

A = \(\frac{171}{134}\)

A​=0,125 • 4 • 16/9•4/5•27/8=12/5

\(A=\left(0,25\right)^{-1}.\left(\frac{1}{4}\right)^{-2}.\left(\frac{4}{3}\right)^2.\left(\frac{5}{4}\right)^{-1}.\left(\frac{2}{3}\right)^{-3}\)

\(\Rightarrow A=4^1.4^2.\frac{16}{9}.\frac{4}{5}\frac{27}{8}\)

\(\Rightarrow A=\frac{64}{1}.\frac{16}{9}.\frac{4}{5}.\frac{27}{8}\)

\(\Rightarrow A=\frac{1536}{5}\)

Vậy \(A=\frac{1536}{5}\)