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.

câu thứ hai là (-2) mũ 3 nhé

\(25\cdot\left(-\frac{1}{3}\right)^3+\frac{1}{5}-2\cdot\left(-\frac{1}{2}\right)^2-\frac{1}{2}\)

\(=25\cdot\frac{-1}{27}+\frac{1}{5}-2\cdot\frac{\left(-1\right)^2}{2^2}-\frac{1}{2}\)

\(=\frac{-25}{27}+\frac{1}{5}-2\cdot\frac{1}{4}-\frac{1}{2}\)

\(=\frac{-98}{135}-\frac{1}{2}-\frac{1}{2}=\frac{-233}{135}\)

\(\left(-2\right)\left(\frac{3}{4}-0,25\right):\left(2\frac{1}{4}-1\frac{1}{6}\right)\)

\(=\left(-2\right)\left(\frac{3}{4}-\frac{25}{100}\right):\left(\frac{9}{4}-\frac{7}{6}\right)\)

\(=\left(-2\right)\left(\frac{75}{100}-\frac{25}{100}\right):\left(\frac{27}{12}-\frac{14}{12}\right)\)

\(=\left(-2\right)\cdot\frac{50}{100}:\frac{13}{12}\)

\(=\left(-2\right)\cdot\frac{1}{2}:\frac{13}{12}\)

\(=-1\cdot\frac{12}{13}=-\frac{12}{13}\)

A \(=\frac{35}{6}.\left(\frac{-30}{31}\right)-\frac{11}{31}=\frac{-175}{31}-\frac{11}{31}=\frac{-186}{31}=-6\)

\(B=-60:\left(\frac{-1}{2}\right)+\frac{7}{4}=30+\frac{7}{4}=\frac{127}{4}\)

\(A=\left(3\dfrac{1}{3}+2,5\right):\left(3\dfrac{1}{6}-4\dfrac{1}{5}\right)-\dfrac{11}{31}\\ =\left(\dfrac{10}{3}+\dfrac{5}{2}\right):\left(\dfrac{19}{6}-\dfrac{21}{5}\right)-\dfrac{31}{11}\\ =\left(\dfrac{30}{6}+\dfrac{15}{6}\right):\left(\dfrac{95}{30}-\dfrac{126}{30}\right)-\dfrac{31}{11}\\ =\dfrac{45}{6}:\dfrac{-21}{30}-\dfrac{31}{11}\\ =\dfrac{15}{2}\times\dfrac{-10}{7}-\dfrac{31}{11}=-\dfrac{75}{7}-\dfrac{31}{11}=-\dfrac{825}{77}-\dfrac{217}{77}=\dfrac{-1042}{77}\)

\(B=\left(-6\right).10:\left[-0,25+\dfrac{1}{2}:\left(-2\right)\right]+1\dfrac{3}{4}\\ =-60:\left(\dfrac{-1}{4}+\dfrac{1}{2}.\dfrac{-1}{2}\right)+1\dfrac{3}{4}\\ =-60:\left(\dfrac{-1}{4}+\dfrac{-1}{4}\right)+1\dfrac{3}{4}\\ =-60:\left(\dfrac{-1}{2}\right)+1\dfrac{3}{4}=120+1\dfrac{3}{4}=121\dfrac{3}{4}\)

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) \(A=\left(1:\frac{1}{4}\right).4+25\left(1:\frac{16}{9}:\frac{125}{64}\right):\left(-\frac{27}{8}\right)\)

\(=4.4+25.\frac{36}{125}:\frac{-27}{8}\)

\(=16-\frac{32}{15}=\frac{240}{15}-\frac{32}{15}=\frac{208}{15}\)

b, \(2^n\left(2^{-1}+4\right)=9\cdot2^5\)

=> \(2^n\cdot\frac{9}{2}=9\cdot2^5\)

=> \(2^n=2^6\)

Vậy \(n=6\left(tm\right)\)

a, \(A=4\cdot16\cdot\frac{9}{16}\cdot\frac{4}{5}\cdot\frac{27}{8}=\frac{486}{5}=97,2\)