Bài 5: Lũy thừa của một số hữu tỉ

\(\dfrac{6^2\cdot3^3}{12^2}\)

\(=\dfrac{2^2\cdot3^2\cdot3^3}{2^4\cdot3^2}\)

\(=\dfrac{2^2\cdot3^5}{2^4\cdot3^2}\)

\(=\dfrac{1\cdot3^3}{2^2\cdot1}\)

\(=\dfrac{3^3}{2^2}\)

\(=\dfrac{27}{4}\)

6

a

Xét 2 số hữu tỉ thấy \(-\dfrac{5}{8}\) có tử số -5 là số âm và \(\dfrac{1}{3}\) có tử số 1 là số dương.

=> \(-\dfrac{5}{8}< \dfrac{1}{3}\)

b

Xét 2 số hữu tỉ thấy \(\dfrac{1960}{1961}\) có tử số < mẫu số và \(\dfrac{2021}{2020}\) có tử số > mẫu số.

=> \(\dfrac{1960}{1961}< \dfrac{2021}{2020}\)

c

\(\dfrac{8}{3}=\dfrac{32}{12};\dfrac{13}{4}=\dfrac{39}{12}\)

\(\dfrac{31}{12}< \dfrac{39}{12}\Rightarrow\dfrac{8}{3}< \dfrac{13}{4}\)

7:
2/5=0,4; -4/5=-0,8

-1/4=-0,25

=>-2<-4/5<-1/4<0<2/5

6:

a: -5/8<0<1/3

b: 1960/1961<1

2021/2020>1

=>1960/1961<2021/2020

c: 8/3<3

13/4>3

=>8/3<13/4

1: Số đối của 1 là -1

Số đối của 1,2 là -1,2

Số đối của -15/24 là 15/24

Số đối của -0,25 là 0,25

Số đối của \(-5\dfrac{1}{4}\) là 21/4

5:

a: -3/4=-15/20

-4/5=-16/20

mà -15>-16

nên -3/4>-4/5

b: -0,25=-1/4=1/-4

c: \(-2\dfrac{1}{4}=-\dfrac{2\cdot4+1}{4}=-\dfrac{9}{4}=\dfrac{9}{-4}\)

2: 4/-5; -8/10; 16/-20

1: \(-35\in Q;17\in Z;9\in Q;\dfrac{-5}{12}\notin N\)

\(\dfrac{12}{19}\notin Z;\dfrac{7}{-8}\in Q;-12,5\notin Z;0,125\in Q\)

BÀI 1:

Uaa cái này mình giải rồi mà c oii ;-;;.

https://hoc24.vn/cau-hoi/.8090552870309

a: =>2/3-4x=1/10

=>4x=17/30

=>x=17/120

b: =>2/3:x=-5/4-1/2=-7/4

=>x=-2/3:7/4=-2/3*4/7=-8/21

c: =>0,75x/0.75=0,01/2,5=1/250

=>x=1/250

d: =>3,8:2x=3/32

=>2x=608/15

=>x=304/15

e: =>16/9:[(1-x)*3/2+1/4*4/5]=5/9

=>(1-x)*3/2+1/5=16/9:5/9=16/5

=>(1-x)*3/2=3

=>1-x=3:3/2=2

=>x=-1

a: \(=\dfrac{-6\left(\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{31}\right)}{9\left(\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{31}\right)}=\dfrac{-6}{9}=\dfrac{-2}{3}\)

b: \(=\dfrac{\dfrac{1}{9}-\dfrac{1}{7}-\dfrac{1}{11}}{4\left(\dfrac{1}{9}-\dfrac{1}{7}-\dfrac{1}{11}\right)}+\dfrac{3\left(\dfrac{1}{5}-\dfrac{1}{25}-\dfrac{1}{125}-\dfrac{1}{625}\right)}{4\left(\dfrac{1}{5}-\dfrac{1}{25}-\dfrac{1}{125}-\dfrac{1}{625}\right)}\)

=1/4+3/4

=1

c: \(=\left[\dfrac{4-3}{386}\cdot\dfrac{193}{17}+\dfrac{33}{34}\right]:\left[\dfrac{14+11}{4002}\cdot\dfrac{2001}{25}+\dfrac{9}{2}\right]\)

\(=\left(\dfrac{1}{34}+\dfrac{33}{34}\right):\left(\dfrac{1}{2}+\dfrac{9}{2}\right)\)

=1/5

c) \(\left[\left(\dfrac{2}{193}-\dfrac{3}{386}\right)\cdot\dfrac{193}{17}+\dfrac{33}{34}\right]:\left[\left(\dfrac{7}{2001}+\dfrac{11}{4002}\right)\cdot\dfrac{2001}{25}+\dfrac{9}{2}\right]\)

\(=\left[\left(\dfrac{4}{386}-\dfrac{3}{386}\right)\cdot\dfrac{193}{17}+\dfrac{33}{34}\right]:\left[\left(\dfrac{14}{4002}+\dfrac{11}{4002}\right)\cdot\dfrac{2001}{25}+\dfrac{9}{2}\right]\)

\(=\left(\dfrac{1}{386}\cdot\dfrac{193}{17}+\dfrac{33}{34}\right):\left(\dfrac{25}{4002}\cdot\dfrac{2001}{25}+\dfrac{9}{2}\right)\)

\(=\left(\dfrac{193}{6562}+\dfrac{33}{34}\right):\left(\dfrac{2001}{4002}+\dfrac{9}{2}\right)\)

\(=\left(\dfrac{1}{34}+\dfrac{33}{34}\right):\left(\dfrac{1}{2}+\dfrac{9}{2}\right)\)

\(=\dfrac{34}{34}:\dfrac{10}{2}\)

\(=1:5=\dfrac{1}{5}\)

a) \(\dfrac{\dfrac{-6}{7}+\dfrac{6}{19}-\dfrac{6}{31}}{\dfrac{9}{7}-\dfrac{9}{19}+\dfrac{9}{31}}\)

\(=\dfrac{-6\left(\dfrac{1}{7}-\dfrac{1}{19}+\dfrac{1}{31}\right)}{9\left(\dfrac{1}{7}-\dfrac{1}{19}+\dfrac{1}{31}\right)}\)

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

\(=-\dfrac{2}{3}\)

`@` `\text {Ans}`

`\downarrow`

`a)`

`(-2/3)^2*(-2/3)`

`= (-2/3)^3 = -8/27`

`b)`

`(-2/5)^3 \div -2/5`

`= (-2/5)^2 = 4/25`

`c)`

`(1,5)^5 \div (1,5)^2`

`= (1,5)^3 = 3,375`

`d)`

`(0,25)^3*(0,25)^2`

`= (0,25)^5 = 1/1024`

`a,=((-2)/3)^3=(-2)^3/3^3=-8/27`

`b,=((-2)/5)^2=(-2)^2/(5^2)=4/25`

`c,=(1,5)^3=(3/2)^3=3^3/2^3=27/8`

`d,=(0,25)^5=(1/4)^5=1^5/4^5=1/1024`

\(a)\left(\dfrac{-2}{3}\right)^2\cdot\dfrac{-2}{3}\\ =\dfrac{\left(-2\right)^2}{3^3}\cdot\dfrac{-2}{3}\\ =\dfrac{4}{9}\cdot\dfrac{-2}{3}\\ =\dfrac{-8}{27}\\ b)\left(\dfrac{-2}{5}\right)^3\cdot\dfrac{-2}{5}\\ =\dfrac{\left(-2\right)^3}{5^3}\cdot\dfrac{-2}{5}\\ =\dfrac{-8}{125}\cdot\dfrac{-2}{5}\\ =\dfrac{16}{625}\\ c)\left(1,5\right)^5:\left(1,5\right)^2\\ =\left(1,5\right)^{5-2}\\ =\left(1,5\right)^3\\ =\left(\dfrac{3}{2}\right)^3\\ =\dfrac{3^3}{2^3}\\ =\dfrac{27}{8}\\ d)\left(0,25\right)^3.\left(0,25\right)^2\\ =\left(0,25\right)^{3+2}\\ =\left(0,25\right)^5\\ =\left(\dfrac{1}{4}\right)^5\\ =\dfrac{1^5}{4^5}\\ =\dfrac{1}{1024}\)

đường kính TĐ = 142796/10 = 14279,6 ( km )

khối lượng TĐ = 1,9x10^27/318 = 597 x 10^22

tương tự nhé 

`@` `\text {Ans}`

`\downarrow`

`a)`

\((x-1)^3=27\)

`=> (x-1)^3=3^3`

`=> x-1=3`

`=> x=3+1`

`=> x=4`

Vậy, `x=4`

`b)`

\((2x+1)^2=25\)

`=> (2x+1)^2=(+-5)^2`

`=>`\(\left[{}\begin{matrix}2x+1=5\\2x+1=-5\end{matrix}\right.\)

`=>`\(\left[{}\begin{matrix}2x=4\\2x=-6\end{matrix}\right.\)

`=>`\(\left[{}\begin{matrix}x=2\\x=-3\end{matrix}\right.\)

Vậy, `x \in {2; -3}`

`c)`

\(5^{x+2}=625\)

`=>`\(5^{x+2}=5^4\)

`=> x+2=4`

`=> x=4-2`

`=> x=2`

Vậy, `x=2.`

8:

a: =>x-1=3

=>x=4

b: =>2x+1=5 hoặc 2x+1=-5

=>x=2 hoặc x=-3

c: =>x+2=4

=>x=2

12*10^15 byte bằng:

12*10^15:1:10^9=12*10^6(GB)