\(720:\left[41-\left(2x-5\right)\right]=2^2.5\\ =>720:\left(41-2x+5\right)=4.5=20\\ =>46-2x=720:20=36\\ =>2x=46-36=10\\ =>x=5\)

\(720:\left[41-\left(2x-5\right)\right]=2^2\cdot5\)

\(\Rightarrow720:\left[41-\left(2x-5\right)\right]=4\cdot5\)

\(\Rightarrow720:\left[41-\left(2x-5\right)\right]=20\)

\(\Rightarrow41-\left(2x-5\right)=720:20\)

\(\Rightarrow41-\left(2x-5\right)=36\)

\(\Rightarrow2x-5=41-36\)

\(\Rightarrow2x-5=5\)

\(\Rightarrow2x=5+5\)

\(\Rightarrow2x=10\)

\(\Rightarrow x=\dfrac{10}{2}\)

\(\Rightarrow x=5\)

A=(7+7³).(1+7+7²+7³+..+7⁹)

=350.B

Vì 350 chia hết cho 10 nên A chia hết cho 10

=

Lời giải:
$x+(x+1)+(x+2)+.....+(x+49)+50+51=1776$

$[\underbrace{(x+x+....+x)}_{50}+(1+2+3+....+49)]+50+51=1776$

$x\times 50+(1+2+3+....+50+51)+1776$

$x\times 50+51\times 52:2=1776$

$x\times 50+1326=1776$

$x\times 50=450$

$x=450:50=9$

Đặt: \(A=9^9+9^{10}+...+9^{20}\) 

\(9A=9\cdot\left(9^9+9^{10}+...+9^{20}\right)\)

\(9A=9^{10}+9^{11}+...+9^{21}\)

\(9A-A=9^{10}+9^{11}+...+9^{21}-9^9-9^{10}-...-9^{20}\)

\(8A=9^{21}-9^9\)

\(A=\dfrac{9^{21}-9^9}{8}\)

Đặt $A=9^9+9^{10}+...+9^{20}$

$9\cdot A=9\cdot(9^9+9^{10}+...+9^{20})$

$9A=9^{10}+9^{11}+...+9^{21}$

$9A-A=(9^{10}+9^{11}+...+9^{21})-(9^9+9^{10}+...+9^{20})$

$8A=9^{21}-9^9$

$\Rightarrow A=\dfrac{9^{21}-9^9}{8}$

\(4\cdot5^2-3\cdot2^3+3^3\cdot3^2\)

\(=4\cdot25-3\cdot8+3^{2+3}\)

\(=100-24+3^5\)

\(=100-24+243\)

\(=343-24\)

\(=319\)

3n + 5 chia hết cho 2n + 1 

⇒ 2(3n + 5) chia hết cho 2n + 1

⇒ 6n + 10 chia hết cho 2n + 1

⇒ 6n + 3 + 7 chia hết cho 2n + 1

⇒ 3(2n + 1) + 7 chia hết cho 2n + 1

⇒ 7 chia hết cho 2n + 1

⇒ 2n + 1 ∈ Ư(7) = {1; -1; 7; -7} 

⇒ n ∈ {0; -1; 3; -4}

Mà: n ∈ N

⇒ n ∈ {0; 3} 

\(A=24\cdot6^3\)

\(A=4\cdot6\cdot\left(2\cdot3\right)^3\)

\(A=2^2\cdot2\cdot3\cdot2^3\cdot3^3\)

\(A=\left(2^2\cdot2\cdot2^3\right)\cdot\left(3\cdot3^3\right)\)

\(A=2^6\cdot3^4\)

A = 24.6³

A  = 2³.3.2³.3³

A = 2⁶.3⁴

\(A=2+2^2+...+2^{60}\)

\(A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{59}+2^{60}\right)\)

\(A=2\cdot3+2^3\cdot3+...+2^{59}\cdot3\)

\(A=3\cdot\left(2+2^3+...+2^{59}\right)\)

Vậy A chia hết cho 3 

_______________

\(A=2+2^2+2^3+...+2^{60}\)

\(A=\left(2+2^3\right)+\left(2^2+2^4\right)+...+\left(2^{58}+2^{60}\right)\)

\(A=2\cdot5+2^2\cdot5+...+2^{58}\cdot5\)

\(A=5\cdot\left(2+2^2+...+2^{58}\right)\)

Vậy A ⋮ 5

___________________

\(A=2+2^2+2^3+...+2^{60}\)

\(A=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+...+\left(2^{58}+2^{59}+2^{60}\right)\)

\(A=2\cdot7+2^4\cdot7+...+2^{58}\cdot7\)

\(A=7\cdot\left(2+2^4+...+2^{58}\right)\)

Vậy A ⋮ 7 

\(24\cdot\left(x-16\right)=144\)

\(\Rightarrow x-16=\dfrac{114}{24}\)

\(\Rightarrow x-16=6\)

\(\Rightarrow x=6+16\)

\(\Rightarrow x=22\)

Vậy: \(x=22\)

24 . ( x - 16 ) = 144

        ( x - 16 ) = 144 : 24

         x - 16     = 6 

         x.           =  6 + 16

         x.           = 22