b: \(\left(-0,25\right)^3:\left(-0,25\right)=\left(-0,25\right)^{3-1}=\left(-0,25\right)^2=\left(-\frac14\right)^2=\frac{1}{16}\)

c: \(\left\lbrack\left(-0,5\right)^2\right\rbrack^2=\left\lbrack\left(\frac12\right)^2\right\rbrack^2=\left(\frac12\right)^4=\frac{1}{16}\)

d: \(a^5\cdot a^2=a^{5+2}=a^7\)

f: \(\frac{3^2}{\left(0,375\right)^2}=\left(\frac{3}{0,375}\right)^2=8^2=64\)

e: \(\left(\frac15\right)^5\cdot5^5=\left(\frac15\cdot5\right)^5=1^5=1\)

g: \(\frac{120^3}{40^3}=\left(\frac{120}{40}\right)^3=3^3=27\)

h: \(\left(0,125\right)^3\cdot512=\left(\frac18\right)^3\cdot8^3=1\)

\(A=\frac{4}{5}.\frac{3}{5}.\frac{2}{5}.....\frac{-4}{5}\)

Hội con 🐄 chúc bạn học tốt!!! 

a) 51 1/5 . 3/8 + 27 1/5 . -3/8 + 19

= ( 51 1/5 + 27 1/5 ) . -1 + 19

= (  51 + 27 1/5 )   . -1 + 19

=       78 1/5         .  -1  + 19

=      391/5         .     -1  + 19

=         -391/5                + 19

=              -106/15

b) 1/6 . ( -2 3/2 ) + 1 2/3 . ( -13/5 )

= 1/6  .    -13/5   +  5/3   .    -13/5

= 1/6 . 5/3 . ( -13/5 + -13/5 )

= 1/6 . 5/3 . -26/5

=  1.5.-26 / 6 . 3 . 5

=      -13/30

\(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}+\frac{4}{5}-\frac{5}{6}+\frac{6}{7}+\frac{5}{6}-\frac{4}{5}+\frac{3}{4}-\frac{2}{3}+\frac{1}{2}\)

\(=\left(\frac{1}{2}+\frac{1}{2}+\frac{6}{7}\right)+\left(\frac{2}{3}-\frac{2}{3}\right)+\left(\frac{-3}{4}+\frac{3}{4}\right)+\left(\frac{4}{5}-\frac{4}{5}\right)+\left(\frac{-5}{6}+\frac{5}{6}\right)\)

\(=\frac{13}{7}+0+0+0+0\)

\(=\frac{13}{7}\)

\(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}+\frac{4}{5}-\frac{5}{6}+\frac{6}{7}+\frac{5}{6}-\frac{4}{5}+\frac{3}{4}-\frac{2}{3}+\frac{1}{2}.\)

\(=\left(\frac{1}{2}+\frac{1}{2}\right)+\left(\frac{2}{3}-\frac{2}{3}\right)-\left(\frac{3}{4}-\frac{3}{4}\right)+\left(\frac{4}{5}-\frac{4}{5}\right)-\left(\frac{5}{6}-\frac{5}{6}\right)+\frac{6}{7}\)

\(=1+0-0+0+\frac{6}{7}\)

\(=1+\frac{6}{7}=1\frac{6}{7}\)

25S = 1 - 1/5²+1/5⁴- 1/5⁶+.......+1/5²⁰⁰⁸- 1/5²⁰¹⁰

Cộng 2 vế với S ta có :

26S = 1 - 1/5²⁰¹² < 1  suy ra S< 1/26

\(5^2.S=1-\frac{1}{5^2}+\frac{1}{5^4}-.....+\frac{1}{5^{2008}}-\frac{1}{5^{2010}}\)

\(25S=1-\frac{1}{5^2}+\frac{1}{5^4}-...+\frac{1}{5^{2008}}-\frac{1}{5^{2010}}\)Cộng 2 vế với S ta có 

\(26S=1-\frac{1}{5^{2012}}\)\(\Rightarrow26S< 1\Rightarrow S< \frac{1}{26}\)