\(\left(3^{85}+2^{41}\right)\cdot\left(9^{17}-5^{10}\right)\cdot\left(18-6^2:2^1\right)\\ =\left(3^{85}+2^{41}\right)\cdot\left(9^{17}-5^{10}\right)\cdot\left(18-36:2\right)\\ =\left(3^{85}+2^{41}\right)\cdot\left(9^{17}-5^{10}\right)\cdot\left(18-18\right)\\ =\left(3^{85}+2^{41}\right)\cdot\left(9^{17}-5^{10}\right)\cdot0\\ =0\)

Để `(x+3)\vdots(x+1),` ta có:

`(x+3)\vdots(x+1)`

`=> (x+1)+2\vdots(x+1)`

Vì: `(x+1)\vdots(x+1)` \(\rightarrow\) `(x+1)` thuộc `Ư(2) = {+-1;+-2}`

`=> x = {0;-2;1;-3}`

Vậy: `x={0;-2;1;-3}` thì `(x+3)\vdots(x+1)`

(x+3)⋮(x+1)

x+1+2⋮x+1

2⋮x+1 (Vì x+1⋮x+1)

=> x+1 thuộc Ư(2) = {-1; 1; 2; -2}

=> x thuộc {-2; 0; 1; -3}

Vậy x thuộc {-2, 0; 1; -3}

\(\left(3\cdot4\cdot2^{16}\right)^2:\left(11\cdot2^{13}\cdot4^{11}-16^9\right)\\ =\left(3\cdot2^2\cdot2^{16}\right)^2:\left(11\cdot2^{13}\cdot2^{22}-2^{36}\right)\\ =3^2\cdot2^4\cdot2^{32}:\left(11\cdot2^{35}-2^{36}\right)\\ =3^2\cdot2^{36}:\left[2^{35}\cdot\left(11-2\right)\right]\\ =9\cdot2^{36}:\left(2^{35}\cdot9\right)\\ =9\cdot2^{36}:2^{35}:9\\ =2\)

D={0;4;8;12;16;20}

D={x\(⋮\)4; x<21}

Cách 1:

\(D=\left\{0;4;8;12;16;20\right\}\)

Cách 2:

\(D=\left\{x\in N|x⋮4,x< 21\right\}\)

Để `5n+22 \vdots n+3,` ta có:

`5n +22 \vdots n+3`

`=> 5n + 15 + 7 \vdots n + 3`

`=> 5 (n + 3)  + 7 \vdots n + 3`

Vì:: `5 ( n + 3)\vdots n + 3 -> n  + 3 in Ư(7)={+-1;+-7}`

`=> n = {-2;-4;4;-10}`

Vậy: `n = {-2;-4;4;-10}` thì `5n + 22 \vdots n+3`

\(5n+22⋮n+3\\ \Leftrightarrow5n+15+7⋮n+3\\ \Leftrightarrow7⋮n+3\text{ }\left(\text{Vì 5n + 14 ⋮ n + 3}\right)\\ \Leftrightarrow n+3\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)

\(\Leftrightarrow\left[{}\begin{matrix}n+3=1\\n+3=-1\\n+3=7\\n+3=-7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}n=-2\\n=-4\\n=4\\n=-10\end{matrix}\right.\)

Vậy \(n\in\left\{-2;-4;4;-10\right\}\)

\(\left(2x+1\right)^3=125\\ \Rightarrow\left(2x+1\right)^3=5^3\\ \Rightarrow2x+1=5\\ \Rightarrow2x=5-1\\ \Rightarrow2x=4\\ \Rightarrow x=4:2\\ \Rightarrow x=2\)

\(\left(2x+1\right)^3=125\)

=>\(\left(2x+1\right)^3=5^3\)

=>2x+1=5

=>2x=5-1=4

=>\(x=\dfrac{4}{2}=2\)

y chia 19 được thương là 20, dư là 8

=>\(y=19\cdot20+8=380+8=388\)

1: \(1935⋮5;540⋮5;270⋮5\)

Do đó: \(1935-540+270⋮5\)

\(1935⋮9;540⋮9;270⋮9\)

Do đó: \(1935-540+270⋮9\)

2: \(5^{3x-1}-5^{2x+1}=0\)

=>\(5^{3x-1}=5^{2x+1}\)

=>3x-1=2x+1

=>3x-2x=1+1

=>x=2

C=1x2x3+2x3x4+3x4x5+...+98x99x100
4C=1x2x3x4+2x3x4x4+3x4x5x4+...+98x99x100x4
     =1x2x3x(4-0)+2x3x4x(5-1)+3x4x5x(6-2)+...+98x99x100x(101-97)
    =1x2x3x4-0+2x3x4x5-1x2x3x4+3x4x5x6-2x3x4x5+...+98x99x100x101-97x98x99x100
    =98x99x100x101
C=98x99x100x101:4=98x99x25x101
=> Vậy C = 98 x 99 x 25 x 101