A = (5+5^2+5^3)+(5^4+5^5+5^6)+...+(5^2020+5^2021+5^2022)

= 5(1+5+5^2)+5^4(1+5+5^2)+...+5^2020(1+5+5^2)

= 5.31+5^4.31+...+5^2020.31

= 31(5+5^4+...+5^2020) chia hết cho 31

sossososo

:)))

Ta có \(B=5^{2024}+5^{2023}+5^{2022}\)

\(B=5^{2022}\left(5^2+5+1\right)\)

\(B=31.5^{2022}⋮31\)

Vậy \(B⋮31\) (đpcm)

Bài 1: 

a) 0²⁰⁰² < 0²⁰²³

b) 2022⁰ = 2023⁰

c) 54⁹ < 55¹⁰

d) ( 4 + 5 )³ > 4² + 5²

đ) 9² - 3² > ( 9 - 3 )²

Bài 2:

a) 3² x 4³ - 3² + 333

= 9 x 64 - 9 + 333

= 576 - 9 + 333

= 567 + 333

= 900

b) 5 x 4³ + 24 x 5 + 41⁰

= 5 x 64 + 24 x 5 + 1

= 5 x ( 64 + 24 ) + 1

= 5 x 88 + 1

= 440 + 1

= 441

c) 2³ x 4² + 3² x 5 - 40 x 1²⁰²³

= 8 x 16 + 9 x 5 - 40 x 1

= 128 + 45 - 40

= 133

Bài 1 :

a) \(0^{2002}=0;0^{2023}=0\Rightarrow0^{2002}=0^{2023}\)

b) \(2022^0=1;2023^0=1\Rightarrow2022^0=2023^0\)

c) \(54^9< 55^9;55^9< 55^{10}\Rightarrow54^9< 55^{10}\)

d) \(\left(4+5\right)^3>\left(4+5\right)^2;\left(4+5\right)^2>4^2+5^2\Rightarrow\left(4+5\right)^3>4^2+5^2\)

đ) \(9^2-3^2=81-9=82;\left(9-3\right)^2=6^2=36\Rightarrow9^2-3^2>\left(9-3\right)^2\)

a)\(27.65+27.35+300=27.\left(65+35\right)+300\)

\(=27.100+300=2700+300=3000\)

b)\(3838:\left[\left(190-6.5^2\right):4+3\right]\)

\(=3838:\left[\left(190-6.25\right):4+3\right]\)

\(=3838:\left[\left(190-150\right):4+3\right]\)

\(=3838:\left[40:4+3\right]=3838:\left[10+3\right]\)

\(=3838:13=\dfrac{3838}{13}\)

c)\(2022-x=2021\)

\(x=2022-2021=1\)

d)\(26+14:\left(x-5\right)=33\)

\(14:\left(x-5\right)=33-26=7\)

\(x-5=14+7=2\)

\(x=2+5=7\)

e)đề hỏi làm j thế bạn

Bài 9,

6²x73+36x3³=36x73+36x27=36(73+27)=36x100=3600.

197-\([\)6x(5-1)²+2022⁰\(]\):5=197-\([\)6x16+1\(]\):5=197-97:5=197-97/5=888/5.

Bài 10,

21-4x=13

=>4x=21-13=8

=>x=8:4=2.

30:(x-3)+1=4⁵:4³=4²=16

=>30:(x-3)=16-1=15

=>x-3=30:15=2

=>x=2+3=5.

(x-1)³+5x6=38

=>(x-1)³+30=38

=>(x-1)³=38-30=8=2³

=>x-1=2

=>x=3.

  S= 5+5²+5³+...+5²⁰²⁰+5²⁰²¹

 5S=5²+5³+5⁴+...+5²⁰²¹+5²⁰²²

 5S - S=4S=5²⁰²²-5

  Ta có: 4S+5=5²⁰²²

             =4S -5 +5 =5²⁰²²

              => 4S=5²⁰²²

a) \(9.x-2.x=\frac{6^{27}}{6^{25}}+\frac{48}{12}\)

\(\Leftrightarrow7x=6^2+4\)

\(\Leftrightarrow7x=36+4=40\)

\(\Leftrightarrow x=\frac{40}{7}\)

Vậy : \(x=\frac{40}{7}\)

b) \(11^x=5.x+\frac{5^{31}}{5^{29}}+3.2^2-10^0\)

\(\Leftrightarrow11^x=5x+5^2+12-1\)

\(\Leftrightarrow11^x=5x+36\)

\(\Rightarrow x\in\varnothing\)

`5^2023 : 5^2022 + 4^3 - 75`

`= 5^1 + 64 - 75`

`= 69 - 75`

`= -6`

\(5^{2023}:5^{2022}+4^3-75=5+64-75=69-75-6\)

tôi không biết làm nhưng tính ra kết quả bằng 25

a)-84:4+3^9:3^7+5^0

=-21+(3^9:3^7)+1

=-21+3^2+1

=-21+9+1

=-12+1

=-11

b)295-(31-2^5.5)^2

=295-(31-32.5)^2

=295-(-129)^2

=295+129^2

=295-16641

=-16346

tick cho mk nha bạn

a) -84 : 4 + 3^ 9 : 3 ^ 7 + 5 ^0

=-84:4+3^2+1

=-84:4+9+1

=-21+9+1

=-12+1

=-11

b) 295 - ( 31 - 2^ 5. 5) ^2

= 295 - ( 31 -32. 5)^2

= 295 - (-129)^2

=295-16641

=-16346