=\(\dfrac{-133}{9}\)

\(1024\div2^5+140\div\left(38+5^2\right)-7^{23}\div7^{21}\)

\(=1024\div32+140\div\left(38+25\right)-7^{23}\div7^{21}\)

\(=32+140\div63-7^2\)

\(=32+\dfrac{20}{9}-49\)

\(=\dfrac{308}{9}-49\)

\(=-\dfrac{133}{9}\)

khó dị 

`( x+2 ) +(x+5)+(x+8)+...+(x+59)=670`

`=> (x+x+x+...+x) +(2+5+8+...+59)=670`

Số số hạng là :

`(59-2) : 3+1=1=20`

Tổng dãy là :

`(59+2) * 20 : 2=610`

`20x+610=670`

`=> 20x=670-610`

`=>20x= 60`

`=>x=60:20`

`=>x=3`

\(\left(x+\dfrac{1}{2}\right)^2=\dfrac{4}{9}\\ \Leftrightarrow\left(x+\dfrac{1}{2}\right)^2=\left(\dfrac{2}{3}\right)^2\\ \Leftrightarrow\left[{}\begin{matrix}x+\dfrac{1}{2}=\dfrac{2}{3}\\x+\dfrac{1}{2}=-\dfrac{2}{3}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{6}\\x=-\dfrac{7}{6}\end{matrix}\right.\)

Vậy...

\(\left(x+\dfrac{1}{2}\right)^2=\dfrac{4}{9}\)

\(\left(x+\dfrac{1}{2}\right)^2=\left(\dfrac{2}{3}\right)^2\)

\(x+\dfrac{1}{2}=\dfrac{2}{3}\)

\(x=\dfrac{2}{3}-\dfrac{1}{2}=\dfrac{4}{6}-\dfrac{3}{6}\)

\(=\dfrac{1}{6}\)

Gọi số hạng thứ nhất, thứ hai là a, b khi đó:

\(10a+b=4263\)

\(a+b=1356\)

\(\Rightarrow9a=10a+b-a-b=4263-1356=2907\)

\(\Rightarrow a=2907:9=323\)

Vậy số hạng thứ nhất là 323

\(a,Ư\left(199\right)=\left\{1;199\right\}\\ B,Ư\left(625\right)=\left\{1;5;25;625\right\}\\ c,Ư\left(200\right)=\left\{1;2;4;5;8;10;20;25;40;50;100;200\right\}\)

a,Ư(199)={1;199} 
 

b,Ư(625)={1;5;25;625} 
 

c,Ư(200)={1;2;4;5;8;10;20;25;40;50;100;200} 

\(Ư\left(90\right)=\left\{\text{1,2,3,5,6,9,10,15,18,30,45}\right\}\) 11 ước

\(Ư\left(540\right)=\left\{\text{1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270}\right\}\)

23 ước

\(Ư\left(3675\right)=\left\{\text{1,3,5,7,15,21,25,35,49,75,105,147,175,245,525,735,1225}\right\}\)

17 ước

a. 90 = 2.3.3.5 

Số ước là: 

(1 + 1) x (2 +1) x ( 1 + 1) = 12 

b. 540 = 2.2.3.3.5

Số ước là: 

(2+1).(3+1).(1+1) = 24 

c. 3675 = 3.5.5.7.7

Số ước là: 

( 1 + 1).(2+1).(2+1) = 18 ước 

\(4578=2\cdot3\cdot7\cdot109\)

\(22725=3^2\cdot5^2\cdot101\)

\(478=2\cdot239\)

212 ⋮ 2

522 ⋮ 2

Vậy (212 + 522) ⋮ 2

\(212⋮2\)

\(522⋮2\)

\(\Rightarrow512+522⋮2\)