\(7^{20}+49^{11}+343^7\)

\(=7^{20}+\left(7^2\right)^{11}+\left(7^3\right)^7\)

\(=7^{20}+7^{22}+7^{21}\)

\(=7^{20}\left(1+7^2+7\right)\)

\(=7^{20}.57⋮57\)

\(\Leftrightarrowđpcm\)

$ 7^{20} + 49^{11} + 343^{7} \\ = 7^{20} + (7^{2})^{11} + (7^{3})^{7} \\ = 7^{20} + 7^{22} + 7^{21} \\ = 7^{20}(1 + 49 + 7) \\ = 7^{20} . 57 \vdots 57 $

7^20 + 49^11 + 343^7 = ( 7^1 )^20 + ( 7^2 )^11 + ( 7^3 )^7 

=7^20 + 7^21 + 7^22 = 7^20 ( 1 + 7 + 7^2 ) = 720.57 Vì 57 chia hết cho 57 nên 7^20 .57 chia hết cho 57 => 7^20 + 49^11 + 343^7 chia hết cho 57 

7²⁰ + 49¹¹ + 343⁷ = ( 7¹ )²⁰ + ( 7² )¹¹ + ( 7³ )⁷ =7²⁰ + 7²¹ + 7²² = 7²⁰ ( 1 + 7 + 7² ) = 7²⁰.57

Vì 57 chia hết cho 57 nên 7²⁰ .57 chia hết cho 57 

=> 7²⁰ + 49¹¹ + 343⁷ chia hết cho 57 ( đpcm )

Ta có: 7^20 + 49^11 + 343^7 = 7^20 + (7^2)^11 + (7^3)^7 = 7^20 + 7^22 + 7^21 = 7^20(1 + 7 + 7^2) = 7^20.57 chia hết cho 57

=>ĐPCM

Ta có: 7²⁰+49¹¹+343⁷= 7²⁰+(7²)¹¹+ (7³)⁷

= 7²⁰+7²²+7²¹=7²⁰.(1+7+7²)=7²⁰.57 chia hết cho 57

\(\Rightarrow\)7²⁰+49¹¹+343⁷ chia hết cho 57

\(\left(\dfrac{6:\dfrac{3}{5}-\dfrac{17}{16}.\dfrac{6}{7}}{\dfrac{21}{5}.\dfrac{10}{11}+\dfrac{57}{11}}-\dfrac{\left(\dfrac{3}{20}+\dfrac{1}{2}-\dfrac{1}{15}\right).\dfrac{12}{49}}{\dfrac{10}{3}+\dfrac{2}{9}}\right).x=\dfrac{215}{96}\)

\(\Rightarrow\left(\dfrac{\dfrac{509}{56}}{9}-\dfrac{\dfrac{7}{12}.\dfrac{12}{49}}{\dfrac{32}{9}}\right).x=\dfrac{215}{96}\)

\(\Rightarrow\left(\dfrac{509}{504}-\dfrac{\dfrac{1}{7}}{\dfrac{32}{9}}\right).x=\dfrac{215}{96}\)

\(\Rightarrow\left(\dfrac{509}{504}-\dfrac{9}{224}\right).x=\dfrac{215}{96}\)

\(\Rightarrow\dfrac{1955}{2016}.x=\dfrac{215}{96}\)

\(\Rightarrow x=\dfrac{215}{96}:\dfrac{1955}{2016}\)

\(\Rightarrow x=\dfrac{903}{391}\)

`[ 6 : 3/5 - 17/16 . 6/7 : 21/5 . 10/11 + 57/11 -  (3/20 + 1/2 - 1/15) . 12/49 :  10/3 + 2/9 ] . x = 215/96`

`=>[ 6  . 5/3 - 17/16 . 6/7 . 5/21 . 10/11 + 57/11 -  (3/20 + 1/2 - 1/15) . 12/49 . 3/10 + 2/9 ] . x = 215/96`

`=>[10- 51/56 . 6/7 . 5/21 . 10/11 + 57/11 -  (3/20 + 1/2 - 1/15) . 12/49 . 3/10 + 2/9 ] . x = 215/96`

`=> [10- 153/196  . 5/21 . 10/11 + 57/11 -  (3/20 + 1/2 - 1/15) . 12/49 . 3/10 + 2/9 ] . x = 215/96`

`=> [10- 255/1372 . 10/11 + 57/11 -  (3/20 + 1/2 - 1/15) . 12/49 . 3/10 + 2/9 ] . x = 215/96`

`=> [10- 1275/7546 + 57/11 -  (3/20 + 1/2 - 1/15) . 12/49 . 3/10 + 2/9 ] . x = 215/96`

`=> (10- 1275/7546 + 57/11 -  7/12. 12/49 . 3/10 + 2/9 ) . x = 215/96`

`=> ( 10- 1275/7546 + 57/11 -343/600 . 3/10 + 2/9 ) . x = 215/96`

`=> ( 10- 1275/7546 + 57/11 -343/2000 + 2/9 ) . x = 215/96`

`=>15,06357671 . x= 215/96`

`=> x= 215/96: 15,06357671`

`=>x= 0,1486754027`

Đề có phải như vậy không nhỉ ?

1)\(8.2^n=128\Rightarrow2^n=128:8\Rightarrow2^n=16\Rightarrow2^n=2^4\Rightarrow n=4\)

2)\(121.11^n=1331\Rightarrow11^n=1331:121\Rightarrow11^n=11\Rightarrow n=1\)

3)\(7^n:49=343\Rightarrow7^n:7^2=7^3\Rightarrow7^n=7^3.7^2\Rightarrow7^n=7^5\Rightarrow n=5\)

nhớ **** cho mình nhé