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`Answer:`

\(A=\left(1^{100}+2^{100}+...+10^{100}\right)\left(5^{10}-25^5\right)\)

\(=\left(1^{100}+2^{100}+...+10^{100}\right)[5^{10}-\left(5^2\right)^5]\)

\(=\left(1^{100}+2^{100}+...+10^{100}\right)\left(5^{10}-5^{10}\right)\)

\(=\left(1^{100}+2^{100}+...+10^{100}\right).0\)

\(=0\)

\(B=\left(2^5+3^5+4^5\right)\left(1^2+2^2+...+100^2\right)\left(4^{10}-2^{20}\right)\)

\(=\left(2^5+3^5+4^5\right)\left(1^2+2^2+...+100^2\right)\left(2^{2.10}-2^{20}\right)\)

\(=\left(2^5+3^5+4^5\right)\left(1^2+2^2+...+100^2\right).0\)

\(=0\)

\(\dfrac{7}{10}+3:10+\dfrac{2}{5}+1:10\\ =\left(\dfrac{7}{10}+\dfrac{2}{5}\right)+\left(3:10+1:10\right)\\ =\dfrac{11}{10}+\left(3+1\right)\times\dfrac{1}{10}\\ =\dfrac{11}{10}+4\times\dfrac{1}{10}\\ =\dfrac{11}{10}+\dfrac{2}{5}\\ =\dfrac{3}{2}\)

\(\dfrac{7}{10}+3:10+\dfrac{2}{5}+1:10\\ =\dfrac{7}{10}+\dfrac{3}{10}+\dfrac{2}{5}+\dfrac{1}{10}\\ =\left(\dfrac{7}{10}+\dfrac{3}{10}\right)+\left(\dfrac{2}{5}+\dfrac{1}{10}\right)\\ =\dfrac{10}{10}+\left(\dfrac{4}{10}+\dfrac{5}{10}\right)=\dfrac{10}{10}+\dfrac{5}{10}=\dfrac{15}{10}=\dfrac{3}{2}\)

= \(\dfrac{3}{2}\)

\(B=\left(2^5+3^5+4^5\right).\left(1^2+2^2+...+100^2\right).\left(4^{10}-2^{20}\right)\)

=>\(B=\left(2^5+3^5+4^5\right).\left(1^2+2^2+...+100^2\right).\left(\left(2^2\right)^{10}-2^{20}\right)\)

=>\(B=\left(2^5+3^5+4^5\right).\left(1^2+2^2+...+100^2\right).\left(2^{20}-2^{20}\right)\)

=>\(B=\left(2^5+3^5+4^5\right).\left(1^2+2^2+...+100^2\right).0\)

=>B=0

\(2\dfrac{1}{3}.3=\dfrac{7}{3}.3=7.\\ \left(\dfrac{2}{5}-\dfrac{3}{4}\right)-\dfrac{2}{5}=\dfrac{2}{5}-\dfrac{3}{4}-\dfrac{2}{5}=-\dfrac{3}{4}.\\ \dfrac{-10}{11}.\dfrac{4}{7}+\dfrac{-10}{11}.\dfrac{3}{7}+1\dfrac{10}{11}.\\ =\dfrac{-10}{11}\left(\dfrac{4}{7}+\dfrac{3}{7}-1\right).\\ =\dfrac{-10}{11}.\left(1-1\right)=0.\)

1) 2\(\dfrac{1}{3}\).3=\(\dfrac{7}{3}\).3=7.

2) (2/5 -3/4) -2/5 = 2/5 -3/4 -2/5 = -3/4.

3) \(\dfrac{-10}{11}.\dfrac{4}{7}+\dfrac{-10}{11}.\dfrac{3}{7}+1\dfrac{10}{11}=\dfrac{1}{11}\left(-\dfrac{40}{7}-\dfrac{30}{7}+21\right)=\dfrac{1}{11}.\left(-10+21\right)=1\).

1+1/2+2/3+4/5+....+9/10

=(1+1+1+....+1)-(1/2+1/3+1/5+....+1/10)

=10-(1/2+1/3+...+1/10)

phần sau bạn tự làm nhé

\(1+\frac{1}{2}+\frac{2}{3}+...+\frac{9}{10}=\left(1+1+1+...+1\right)-\left(\frac{1}{2}+\frac{1}{3}+....+\frac{1}{10}\right)\)

\(=10-\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right)\)

1+1/2+1/2+....+9/10=(1+1+1+....+1)-(1/2+1/3+1/4.... 1/10)

=10-(1/2+1/3+1/4+....+1/10)

\(\dfrac{17}{5}.\dfrac{-31}{125}.\dfrac{1}{2}.\dfrac{10}{17}.\dfrac{-1}{2^3}\\= \left(\dfrac{17}{5}.\dfrac{10}{17}\right)\left(\dfrac{-31}{125}.\dfrac{-1}{8}\right).\dfrac{1}{2}\\ =2.\dfrac{31}{1000}.\dfrac{1}{2}\\ =\left(2.\dfrac{1}{2}\right).\dfrac{31}{1000}\\ =1.\dfrac{31}{1000}\\ =\dfrac{31}{1000}\)

{[( \(3^2\)+ 1 ) .10-(8:2 + 6 ) ] : 2 } + 55 - ( 10 : 5 )\(^3\)

= {[( 9 + 1 ) . 10 - ( 4 + 6 )] : 2 } + 55 - 2\(^3\)

= {[ 10 . 10        - 10       ]   : 2 }  + 55 - 8

= {[ 100 - 10                  ]    : 2 }  + 47

= { 90  : 2                                  } + 47

= 45 + 47 

= 92

`1/2+2/4+3/6+4/8+5/10+6/12`

`=1/2+1/2+1/2+1/2+1/2+1/2`

`=1/2*6=3`

`1/3+1/4+1/5+8/10+20/15+20/30`

`=(1/3+1/4)+(1/5+4/5)+(4/3+2/3)`

`=7/12+1+2`

`=7/12+3=43/12`

\(\dfrac{1}{2}+\dfrac{2}{4}+\dfrac{3}{6}+\dfrac{4}{8}+\dfrac{5}{10}+\dfrac{6}{12}\)
\(=\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{2}\)
\(=\dfrac{1}{2}\times6=3\)
\(------\)
\(\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{8}{10}+\dfrac{20}{15}+\dfrac{20}{30}\)
\(=\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{4}{5}+\dfrac{4}{3}+\dfrac{2}{3}\)
\(=\left(\dfrac{1}{3}+\dfrac{4}{3}+\dfrac{2}{3}\right)+\left(\dfrac{1}{5}+\dfrac{4}{5}\right)+\dfrac{1}{4}\)
\(=\dfrac{7}{3}+1+\dfrac{1}{4}\)
\(=\dfrac{28}{12}+\dfrac{12}{12}+\dfrac{3}{12}\)
\(=\dfrac{43}{12}\)

`=1/2+1/2+1/2+1/2+1/2+1/2= 1/2 \times 6=3`

`----`

`=1/3+1/4+1/5+4/5+4/3+2/3 =(4/3+2/3+)+(1/5+4/5)+1/3+1/4=2+1+1/3+1/4=3+1/3+1/4=43/12`