\(A=7+7^2+7^3+7^4+7^5+7^6+7^7+7^8\)

\(A=\left(7+7^3\right)+\left(7^2+7^4\right)+\left(7^5+7^7\right)+\left(7^6+7^8\right)\)

\(A=7\cdot\left(7+7^2\right)+7^2\cdot\left(1+7^2\right)+7^5\cdot\left(1+7^2\right)+7^6\cdot\left(1+7^2\right)\)

\(A=7\cdot50+7^2\cdot50+7^5\cdot50+7^6\cdot50\)

\(A=50\cdot\left(7+7^2+7^5+7^6\right)\)

\(A=5\cdot10\cdot\left(7+7^2+7^5+7^6\right)\)

Ta có: 5 ⋮ 5

⇒ \(A=5\cdot10\cdot\left(7+7^2+7^5+7^6\right)\) ⋮ 5 (đpcm) 

A = 7 + 7² + 7³ + 7⁴ + 7⁵ + 7⁶ + 7⁷ + 7⁸

A =  (7 + 7³) + (7²+ 7⁴) + (7⁵ + 7⁷) + (7⁶ + 7⁸)

A = 7.(1 + 7²)  + 7².(1 + 7²) + 7⁵.(1 + 7²) + 7⁶.(1 + 7²)

A = 7.( 1 + 49) + 7².( 1 + 49) + 7⁵.(1 + 49) + 7⁶. (1 + 49)

A = 7.50 + 7².50 + 7⁵.50 + 7⁶.50

A = 50.(7 + 7² + 7⁵ + 7⁶)

Vì 50 ⋮ 5 nên A = 50.(7 + 7² + 7⁶) ⋮ 5 đpcm

a) \(7^6+7^5-7^4=7^4\left(7^2+7-1\right)=7^4\left(49+7-1\right)=7^4.55⋮55\)

b) \(16^5+2^{15}=\left(2^4\right)^5+2^{15}=2^{20}+2^{15}=2^{15}\left(2^5+1\right)=2^{15}\left(32+1\right)=2^{15}.33⋮33\)

c) \(81^7-27^9-9^{13}=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}=3^{28}-3^{27}-3^{26}=3^{26}\left(3^2-3-1\right)=3^{26}.5=3^{22}.3^4.5=3^{22}.405⋮405\)

a: \(=7^4\left(7^2+7-1\right)=7^4\cdot55⋮55\)

b: \(=2^{20}+2^{15}=2^{15}\left(2^5+1\right)=2^{15}\cdot33⋮33\)

c: \(=3^{28}-3^{27}-3^{26}=3^{26}\left(3^2-3-1\right)=3^{26}\cdot5=3^{22}\cdot405⋮405\)

a) 1.2.3.4.5.6...........10 + 324

= 6 ( a) 1.2.3.4.5.7...........10 + 54) chia hết cho 6

=> a) 1.2.3.4.5.6...........10 + 324 chia hết cho 6

b) 19.220 +76  = 19.2.110+2 . 38 = 38( 110+2) chia hết cho 38

=> ) 19.220 +76  chia hết cho 38

c) 15 . 3 . 999 + 49 = 45.999 + 45 + 4 = 45 ( 999 +1) +4 = 45 . 1000 + 4 chia 45 dư 4 

=> 15 . 3 . 999 + 49 ko chia hết cho 45

Bài 1:

a. $=(-25)(-4)(-35)=100(-35)=-3500$

b. $=16-10=6$

c. $=180-(-16)-(-36)=180+16+36=232$

d. $=250-200:[1(-3)^2+(-8)]$

$=250-200:(9-8)=250-200=50$

2.

$60+2(12-x)=-48$

$2(12-x)=60-(-48)=60+48=108$

$12-x=108:2=54$

$x=12-54=-42$
 

Bài 1:

a. $=(-25)(-4)(-35)=100(-35)=-3500$

b. $=16-10=6$

c. $180-(-16)-(-36)=180+16+36=196+36=232$

d. $=250-200:[2000.(-3).2-6]$

$=250-200:[2000.(-6)+(-6)]$

$=250-200:[(-6)(2000+1)]=250-200[(-6).2001]$

$=250+200.6.2001=250+2401200=2401450$

Bài 2:

$60+2(12-x)=-48$

$2(12-x)=-48-60=-108$
$12-x=-108:2=-54$

$x=12-(-54)=66$

A = 8 + 8^2 +8^3 +...+ 8^58+8^59+8^60

   = (8+8^2 + 8^3) +...+ (8^58+8^59 +8^60)

   =8( 1+8+8^2)+...+8^58(1+8+8^2)

   = 8. 73 + ......+8^58 .73

   = 73.( 8+...+8^58) chia hết cho 73

b) Để 4x + 19 chia hết cho x + 1 thì 15 chia hết cho x + 1

--> x + 1 là ước của 15

TH1: x + 1 = 15 <=> x = 14

TH2: x + 1 = 1 <=> x = 0

TH3: x + 1 = 3 <=> x = 2

TH4: x + 1 = 5 <=> x= 4

A=(7+73)+(75+77)+....+(71997+71999)

A=7.(1+72)+75.(1+72)+....+71997.(1+72)

A=7.50+75.50+79.50+.....+71997.50

=>A chia hết cho 5 (1)

A=(7+73+75+....+71999)=7.(70+72+74+....+71998)

=>A chia hết cho 7 (2)

Mà ƯCLN(5;7)=1=>A chia hết cho 35

Ban kia lam dung roi

\(A=\left(1+7\right)+...+7^{2020}\left(1+7\right)=8\left(1+...+7^{2020}\right)⋮8\)

\(A = (1 + 7) +...+7^2\)\(^0\)\(^2\)\(^0\) \((1 + 7) = 8 (1+...+7^2\)\(^0\)\(^2\)\(^0\)\() \) ⋮\(8\)