a) 3² . 5³ + 9² = 9 . 125 + 81

= 1 125 + 81 = 1 206

b) 8³ : 4² - 5² = 512 : 16 - 25 = 32 - 25 = 7

c) 3³ . 9² - 5².9 + 18 : 6 = 27 . 81 - 25 . 9 + 3

= 2 187 - 225 + 3 = 1 962 + 3 = 1 965

 a) 3² . 5³ + 9² = 9 . 125 + 81

= 1 125 + 81 = 1 206

b) 8³ : 4² - 5² = 512 : 16 - 25 = 32 - 25 = 7

c) 3³ . 9² - 5².9 + 18 : 6 = 27 . 81 - 25 . 9 + 3

= 2 187 - 225 + 3 = 1 962 + 3 = 1 965

|(5/8-5/14)+(3/8-9/14)|:4/7

=|(5/8+3/8)+(-5/14-9/14)|:4/7

=|1+(-1)|:4/7

=0

`A = ( 5 / 8 - 5 / 14 ) : 4 / 7 + ( 3 / 8 - 9 / 14 ) : 4 / 7`

`A = ( 5 / 8 - 5 / 14 + 3 / 8 - 9 / 14 ) : 4 / 7`

`A = [ ( 5 / 8 + 3 / 8 ) - ( 5 / 14 + 9 / 14 ) ] . 7 / 4`

`A = ( 8 / 8 - 14 / 14 ) . 7 / 4`

`A = ( 1 - 1 ) . 7 / 4 = 0 . 7 / 4 = 0`

=(1-2-3+4)+(5-6-7+8)+...+(2017-2018-2019+2020)+2021-2022-2023

=0+0+...+0-1-2023

=-2024

Bằng 2024

`A = 2 + 2^2+ ... + 2^2017`

`=> 2A = 2^2 + 2^3 + ... + 2^2018`

`=> 2A - A = (2^2 + 2^3 + ... + 2^2018) - (2 + 2^2 + ... +2^2017)`

`=> A         = 2^2018 - 2`

`B = 1 + 3^2 + ... + 3^2018`

`=> 3^2B = 3^2 + 3^4 + ... + 3^2020`

`=> 9B-B =(3^2 + 3^4 + ... + 3^2020) - (1 + 3^2 + ... + 3^2018`

`=> 8B     = 3^2020 - 1`

`=> B       = (3^2020 - 1)/8`

`C = 5 + 5^2 - 5^3 + ... + 5^2018`

`=> 5C = 5^2 + 5^3 - 5^4 + ... +5^2019`

`=> 5C + C = ( 5^2 + 5^3 - 5^4 + ... 5^2019) + (5 + 5^2 - 5^3 + ... + 5^2018)`

`=> 6C = 55 + 5^2019`

`=> C  = (5^2019 + 55)/6`

a) \(=\dfrac{157}{8}.\dfrac{12}{7}-\dfrac{61}{4}.\dfrac{12}{7}=\dfrac{12}{7}\left(\dfrac{157}{8}-\dfrac{61}{4}\right)=\dfrac{12}{7}.\dfrac{35}{8}=\dfrac{15}{2}\)

b) \(\dfrac{2}{5}.\dfrac{1}{3}-\dfrac{2}{15}\div\dfrac{1}{5}+\dfrac{3}{5}.\dfrac{1}{3}=\dfrac{1}{3}\left(\dfrac{2}{5}+\dfrac{3}{5}\right)-\dfrac{2}{15}.5=\dfrac{1}{3}.1-\dfrac{2}{3}=\dfrac{1}{3}-\dfrac{2}{3}=-\dfrac{1}{3}\)

c) \(=-\dfrac{80}{9}\)

d) \(=-\dfrac{1}{6}\)

2) \(B=\left(1-2-3+4\right)+\left(5-6-7+8\right)+...+\left(1989-1990-1991+1992\right)+1993-1994\)

\(=0+0+...+0+1993-1994=0+1993-1994=-1\)

\(\dfrac{6}{7}+\dfrac{5}{8}:5-\dfrac{3}{16}.\left(-2\right)^2=\dfrac{6}{7}+\dfrac{5}{8}:5-\dfrac{3}{16}.4=\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{3}{4}=\dfrac{5}{56}\)

\(\dfrac{2}{3}+\dfrac{1}{3}.\left(-\dfrac{4}{9}+\dfrac{5}{6}\right):\dfrac{7}{12}=\dfrac{2}{3}+\dfrac{1}{3}.\dfrac{7}{18}:\dfrac{7}{12}=\dfrac{2}{3}+\dfrac{2}{9}=\dfrac{8}{9}\)

a/ A= 1-3+5-7+9-11+......+97-99

      = -2+(-2)+(-2)+......+(-2)

      = (-2).25=-50

b/B=-1-2-3-4-...-100

    =-(1+2+3+4+...+100)

    =-5050

c/C=1-2+3-4+5-6+......+99-100

      = -1+(-1)+(-1)+.............+(-1)

      =(-1).50=-50

d/D=1-2-3+4+5-6-7+8+9-....+94-95

     = (1-2-3+4)+(5-6-7+8)+.......+(92-93-94+95)

    = 0+0+0+...+0=0