Câu a:

CM (7^6 + 7^5 - 7^4) ⋮ 77

7^6 + 7^5 - 7^4

= 7^4.(7^2 + 7 - 1)

= 7^4.(49 + 7 - 1)

= 7^4.(56 - 1)

= 7^4.55

= 7^3.(7.11).5

= 7^3.77.5 ⋮ 77(đpcm)

Câu b:

Cm : (36^36 - 9^10) ⋮ 45

A = 36^36 - 9^10

A = 9^36.4^36 - 9^10

A = 9^10.(9^26.4^36 - 1)

A = 9^10.[(9^2)^13.(4^2)^18 - 1]

A = 9^10.[\(\overline{..1}^{13}\).\(\overline{..6}^{18}\) -1]

A = 9^10.[\(\overline{..6}-\overline{..1}\)]

A = 9^10.\(\overline{..5}\)

A ⋮ 9; 5

9 = 3^2; 5 = 5

BCNN(9; 5) = 45

A ∈ B(45) hay A ⋮ 45 (đpcm)

a)Ta có : 5\(^5\)- 5\(^4\) + 5\(^3\)

= 5³(5² - 5 + 1 )

=5³ . 21 

Vì 21 \(⋮\)7 nên 21 . 5³\(⋮\)7

Vậy 5⁵ -5⁴ + 5³ \(⋮\)7

 Mấy câu kia b giải tương tự nhé

\(e)\) \(81^7-27^9-9^{13}\)

\(=\)\(\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}\)

\(=\)\(3^{28}-3^{27}-3^{26}\)

\(=\)\(3^{24}\left(3^4-3^3-3^2\right)\)

\(=\)\(3^{24}\left(81-27-9\right)\)

\(=\)\(3^{24}.45⋮45\)

Vậy \(81^7-27^9-9^{13}⋮45\)

\(g)\) \(10^9+10^8+10^7\)

\(=\)\(10^6\left(10^3+10^2+10\right)\)

\(=\)\(10^6\left(1000+100+10\right)\)

\(=\)\(10^6.1110\)

\(=10^6.2.555⋮555\)

Vậy \(10^9+10^8+10^7⋮555\)

Chúc bạn học tốt ~ 

a) ta có : \(\overline{ab}\)+\(\overline{ba}\) = (10a+b)+(10b+a)= 11a+11b \(⋮\)11

b) tương tự

Bài 1 :

a/   \(a^3.a^9=a^{3+9}=a^{12}\)

b/\(\left(a^5\right)^7=a^{5.7}=a^{35}\)

c/  \(\left(a^6\right).4.a^{12}=a^{24}.a^{12}.4=a^{24+12}.4=a^{36}.4\)

d/  \(\left(2^3\right)^5.\left(2^3\right)^3=2^{15}.2^9=2^{15+9}=2^{24}\)

e/  \(5^6:5^3+3^3.3^2\)

     \(=5^3+3^5=125+243=368\)

i/ \(4.5^2-2.3^2\)

   \(=2^2.5^2-2.3^2\)

   \(=2^2.25-2^2.14\)

   \(=2^2.\left(25-14\right)\)

   \(=2^2.11\)      

   \(=4.11=44\)

Bài 2 :

a, \(3^8:3^6=3^{8-6}=3^2\)

 \(7^5:7^2=7^{5-2}=7^3\)

 \(19^7:19^3=19^{7-3}=19^4\)

  \(2^{10}.8^3=2^{10}.\left(2^3\right)^3=2^{10}.2^9=2^{19}\)  

\(12^7:6^7=\left(12:6\right)^7=2^7=128\)

\(27^5:81^3=\left(3^3\right)^5:\left(3^4\right)^3=3^{15}:3^{12}=3^3=9\)

a) Ta có 120a + 36b = 12.10a + 12.3b = 12(10a + 3b) \(⋮\)12

b) Ta có 5⁷ - 5⁶ + 5⁵ = 5⁵(5² - 5 + 1) = 5⁵.21 \(⋮\)21

c) Ta có 5²⁰¹² + 5²⁰¹³ + 5²⁰¹⁴ = 5²⁰¹²(1 + 5 + 5²) = 5²⁰¹².31 \(⋮31\) 

d) Ta có 7⁶ + 7⁵ - 7⁴ =  7⁴(7² + 7 - 1) = 7⁴.55 = 7³.7.11.5 = 7³.5.77 \(⋮\)77 

a) Vì \(\hept{\begin{cases}120⋮12\\36⋮12\end{cases}\Rightarrow}\hept{\begin{cases}120a⋮12\\36b⋮12\end{cases}}\Rightarrow\left(120a+36b\right)⋮12\)

b) \(5^7-5^6+5^5=5^5\left(5^2-5+1\right)=5^5\left(25-6+1\right)=21.5^5⋮21\)

c)\(5^{2012}+5^{2013}+5^{2014}=5^{2012}\left(1+5+5^2\right)=5^{2012}\left(1+5+25\right)=31.5^{2012}⋮31\)

d)\(7^6+7^5-7^4=7^4\left(7^2+7-1\right)=7^4\left(49+7-1\right)=55.7^4=11.5.7^4⋮11\)

Dễ thấy : \(7^6+7^5-7^4⋮7\)

mà \(\left(11;7\right)=1\)

\(\Rightarrow7^6+7^5-7^4⋮77\)

1)
\(=\dfrac{\left(2.3\right)^{20}.\left(5^2\right)^{19}}{\left(2^3\right)^7.\left(3^2\right)^{10}.\left(5^3\right)^{13}}\)
\(=\dfrac{2^{20}.3^{20}.5^{38}}{2^{21}.3^{20}.5^{39}}\)
\(=\dfrac{1}{2.5}\)
\(=\dfrac{1}{10}\)

a, 7⁶ +7⁵ - 7⁴ = 7⁴(7² + 7 - 1) = 7⁴ . 55 = 7⁴ . 5 . 11 

Vậy 7⁶ +7⁵ - 7⁴ chia hết cho 11

b, Ta có: 10⁶ - 5⁷ = 2⁶ . 5⁶ - 5⁷ = 5⁶(2⁶ - 5) = 5⁶ . 59

Vậy.... 

Bài 1 :

a, Ta có : \(\left(-123\right)+\left|-13\right|+\left(-7\right)\)

= \(\left(-123\right)+13+\left(-7\right)=\left(-117\right)\)

b, Ta có : \(\left|-10\right|+\left|45\right|+\left(-\left|-455\right|\right)+\left|-750\right|\)

= \(10+45-455+750=350\)

c, Ta có : \(-\left|-33\right|+\left(-15\right)+20-\left|45-40\right|-57\)

= \(\left(-33\right)+\left(-15\right)+20-5-57=-90\)