a: \(\dfrac{18}{24}+\dfrac{35}{-21}-\dfrac{1}{2}\)

\(=\dfrac{3}{4}-\dfrac{5}{3}-\dfrac{1}{2}\)

\(=\dfrac{9-20-6}{12}=\dfrac{-17}{12}\)

b: \(\dfrac{-2}{3}-\dfrac{3}{-4}+\dfrac{5}{-6}\)

\(=-\dfrac{2}{3}+\dfrac{3}{4}-\dfrac{5}{6}\)

\(=\dfrac{-8+9-10}{12}=\dfrac{-9}{12}=\dfrac{-3}{4}\)

c: \(\left(\dfrac{3}{4}+\dfrac{-7}{2}\right)\cdot\left(\dfrac{10}{11}+\dfrac{2}{22}\right)\)

\(=\left(\dfrac{3}{4}-\dfrac{14}{4}\right)\cdot\left(\dfrac{10}{11}+\dfrac{1}{11}\right)\)

\(=-\dfrac{11}{4}\cdot1=-\dfrac{11}{4}\)

d: \(\left(\dfrac{7}{3}-\dfrac{-7}{2}\right):\left(-\dfrac{25}{6}\cdot\dfrac{1}{5}\right)\)

\(=\left(\dfrac{7}{3}+\dfrac{7}{2}\right):\dfrac{-5}{6}\)

\(=\dfrac{35}{6}\cdot\dfrac{6}{-5}=\dfrac{35}{-5}=-7\)

a) \(\dfrac{18}{24}+\dfrac{35}{-21}-\dfrac{1}{2}\)

\(=\dfrac{3}{4}-\dfrac{5}{3}-\dfrac{1}{2}\)

\(=\dfrac{9}{12}-\dfrac{20}{12}-\dfrac{6}{12}\)

\(=\dfrac{-17}{12}\)

b) \(\dfrac{-2}{3}-\dfrac{3}{-4}+\dfrac{5}{-6}\)

\(=\dfrac{-8}{12}+\dfrac{9}{12}-\dfrac{10}{12}\)

\(=\dfrac{-9}{12}\)

\(=\dfrac{-3}{4}\)

c) \(\left(\dfrac{3}{4}+\dfrac{-7}{2}\right).\left(\dfrac{10}{11}+\dfrac{2}{22}\right)\)

\(=\dfrac{-11}{4}.1\)

\(=\dfrac{-11}{4}\)

d) \(\left(\dfrac{7}{3}-\dfrac{-7}{2}\right):\left(-\dfrac{25}{6}.\dfrac{1}{5}\right)\)

\(=\dfrac{35}{6}:\dfrac{-5}{6}\)

\(=-7\)

a, 5/-14. 7/-19=8/38

b, -15/4 .( 16/-25 )=12/5

c, 3/-10 .( -15/-2 )=

d, -5/7 . ( 21/-10 )=-9/4

e, 10/-3. (6/-5)==4

f, 21/-9 . ( -6/14 )=1

g, -10/9 . ( 36/20 )=-2

`4/7+4`

`=4/7+4/1`

`=4/7+28/7`

`=32/7`

__

`3+6/11`

`=33/11+6/11`

`=39/11`

__

`3-5/7`

`=3/1-5/7`

`=21/7-5/7`

`=16/7`

__

`21/9-2`

`=21/9-18/9`

`=3/9`

`=1/3`

__

`15/24+2`

`=15/24+48/24`

`=63/24`

`=21/16`

__

`63/45-20/25`

`=63/45-4/5`

`=63/45-36/45`

`=27/45`

`=9/15`

__

`3/4-2/8`

`=3/4-1/4`

`=2/4`

__

`6/7-5/8`

`=48/56-35/56`

`=13/56`

__

`37/45-5/9`

`=37/45-25/45`

`=12/45`

`=4/15`

__

`46/39-11/13`

`=46/39-33/39`

`=13/39`

`=1/2`

__

`5/12+3/4+1/3`

`=5/12+9/12+4/12`

`=14/12+4/12`

`=18/12`

`=3/2`

__

`1/2+3/7+11/14`

`=7/14+6/14+11/14`

`=13/14+11/14`

`=24/14`

`=12/7`

__

`7/10-(1/5+1/4)`

`=7/10-(4/20+5/20)`

`=7/10-9/20`

`=14/20-9/20`

`=5/20`

`=1/4`

__

`15/4-2/3-3/4`

`=(15/4-3/4)-2/3`

`=12/4-2/3`

`=3-2/3`

`=9/3-2/3`

`=7/3`

a: \(\left(-\dfrac{3}{7}\right)^2=\dfrac{\left(-3\right)^2}{7^2}=\dfrac{9}{49}\)

b: \(\dfrac{5}{17}+\dfrac{-15}{34}\cdot\dfrac{2}{5}\)

\(=\dfrac{5}{17}-\dfrac{15}{5}\cdot\dfrac{2}{34}\)

\(=\dfrac{5}{17}-\dfrac{1}{17}\cdot3=\dfrac{2}{17}\)

c: \(\dfrac{-7}{21}+\left(1+\dfrac{1}{3}\right)\)

\(=-\dfrac{1}{3}+1+\dfrac{1}{3}\)

=1

d: \(\left(-\dfrac{1}{5}+\dfrac{3}{12}\right)+\dfrac{-3}{4}\)

\(=\dfrac{-1}{5}+\dfrac{1}{4}-\dfrac{3}{4}\)

\(=\dfrac{-1}{5}-\dfrac{2}{4}\)

\(=\dfrac{-1}{5}-\dfrac{1}{2}=\dfrac{-7}{10}\)

a) Ta có: \(\dfrac{-5}{7}\left(\dfrac{14}{5}-\dfrac{7}{10}\right):\left|-\dfrac{2}{3}\right|-\dfrac{3}{4}\left(\dfrac{8}{9}+\dfrac{16}{3}\right)+\dfrac{10}{3}\left(\dfrac{1}{3}+\dfrac{1}{5}\right)\)

\(=\dfrac{-5}{7}\cdot\dfrac{3}{2}\cdot\dfrac{21}{10}-\dfrac{3}{4}\cdot\dfrac{56}{3}+\dfrac{10}{3}\cdot\dfrac{8}{15}\)

\(=\dfrac{-9}{4}-14+\dfrac{16}{9}\)

\(=\dfrac{-1621}{126}\)

b) Ta có: \(\dfrac{17}{-26}\cdot\left(\dfrac{1}{6}-\dfrac{5}{3}\right):\dfrac{17}{13}-\dfrac{20}{3}\left(\dfrac{2}{5}-\dfrac{1}{4}\right)+\dfrac{2}{3}\left(\dfrac{6}{5}-\dfrac{9}{2}\right)\)

\(=\dfrac{-17}{26}\cdot\dfrac{13}{17}\cdot\dfrac{-3}{2}-\dfrac{20}{3}\cdot\dfrac{3}{20}+\dfrac{2}{3}\cdot\dfrac{-33}{10}\)

\(=\dfrac{3}{4}-1-\dfrac{11}{5}\)

\(=-\dfrac{49}{20}\)

2:

a: \(2^2\cdot3-4=4\cdot3-4=12-4=8\)

b: \(16-2^3\cdot2=16-2^4=16-16=0\)

c: \(4^2-4\cdot2=16-8=8\)

d: \(3^3-2\cdot3^2=27-2\cdot9=27-18=9\)

e: \(7^2-9\cdot2^2=49-9\cdot4=49-36=13\)

f: \(2^2\cdot3+4^2=4\cdot3+16=12+16=28\)

Bài 1:

a: \(13+21\cdot5-\left(198:11-8\right)\)

\(=13+105-18+8\)

=21+87

=108

b: \(272:16-5+4\cdot\left(30-5-255:17\right)\)

\(=17-5+4\cdot\left(30-5-15\right)\)

\(=12+4\cdot10=12+40=52\)

c: \(15\cdot24-14\cdot5\cdot\left(145:5-27\right)\)

\(=360-70\left(29-27\right)\)

=360-140

=220

d: \(18\cdot3-18\cdot2+3\cdot\left(\dfrac{51}{17}\right)\)

\(=18\left(3-2\right)+3\cdot3\)

=18+9

=27

e: \(64+115+36-25\cdot8\cdot6\cdot2^2\cdot3+4^2\)

\(=100+115-200\cdot6\cdot4\cdot3+16\)

\(=231-14400=-14169\)

f: \(15\cdot8-\left(17-30+83\right)-144:6\)

\(=120-24-\left(100-30\right)\)

=96-70

=26

1) a) 4⁸.2²⁰ = (2²)⁸.2²⁰

= 2¹⁶.2²⁰ = 2³⁶

-----------

9¹².27⁵.81³ = (3²)¹².(3³)⁵.(3⁴)⁴

= 3²⁴.3¹⁵.3¹⁶ = 3⁵⁵

--------

64³.4⁵.16² = (4³)³.4⁵.(4²)²

= 4⁹.4⁵.4⁴ = 4¹⁸

b) 25²⁰.125⁴ = (5²)²⁰.(5³)⁴

= 5⁴⁰.5¹² = 5⁵²

--------

x⁷.x³.x⁴ = x¹⁴

--------

3⁶.4⁶ = (3.4)⁶ = 12⁶

2) a) 2² = 4

2³ = 8

2⁴ = 16

2⁵ = 32

2⁶ = 64

2⁷ = 128

2⁸ = 256

2⁹ = 512

2¹⁰ = 1024

b) 3² = 9

3³ = 27

3⁴ = 81

3⁵ = 243

c) 4² = 16

4³ = 64

4⁴ = 256

d) 5² = 25

5³ = 125

5⁴ = 625

3)

a) 4⁹ : 4⁴ = 4⁵

17⁸ : 17⁵ = 17³

2¹⁰ : 8² = 2¹⁰ : (2³)² = 2¹⁰ : 2⁶ = 2⁴

18¹⁰ : 3¹⁰ = (18 : 3)¹⁰ = 6¹⁰

27⁵ : 81³ = (3³)⁵ : (3⁴)³ = 3¹⁵ : 3¹² = 3³

b) 10⁶ : 100 = 10⁶ : 10² = 10⁴

5⁹ : 25³ = 5⁹ : (5²)³ = 5⁹ : 5⁶ = 5³

4¹⁰ : 64³ = 4¹⁰ : (4³)³ = 4¹⁰ : 4⁹ = 4

2²⁵ : 32⁴ = 2²⁵ : (2⁵)⁴ = 2²⁵ : 2²⁰ = 2⁵

18⁴ : 9⁴ = (18 : 9)⁴ = 2⁴

1) x - 2 = -6

x = -6 + 2

x = -4

2) -5 . x - ( -3 ) =13

-5 . x = 13 + ( -3 )

-5 . x = 10

x = 10 : ( -5 )

x = -2