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

a) Ta có: 

\(8^{10}-8^9-8^8=8^8.\left(8^2-8-1\right)=8^8.55⋮55\)

\(\Rightarrow8^{10}-8^9-8^8⋮55\)

b) Ta có:

\(10^9+10^8+10^7=10^7.\left(10^2+10+1\right)=10^7.111⋮111\)

\(\Rightarrow10^9+10^8+10^7⋮111\)

\(8^{10}-8^9-8^8=8^8\left(8^2-8-1\right)=8^8\times55⋮55\)

\(10^9+10^8+10^7=10^7\left(10^2+10+1\right)=10^7\times111⋮111\)

\(e)\) \(81^7-27^9-9^{13}\)

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

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

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

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

\(=\)\(3^{24}.45⋮45\)

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

Ta có : 

\(A=1+5+5^2+...+5^{32}\)

\(A=\left(1+5+5^2\right)+\left(5^3+5^4+5^5\right)+...+\left(5^{30}+5^{31}+5^{32}\right)\)

\(A=31+5^3\left(1+5+5^2\right)+...+5^{30}\left(1+5+5^2\right)\)

\(A=31+31.5^3+...+31.5^{30}\)

\(A=31\left(1+5^3+...+5^{30}\right)\) chia hết cho 31 

Vậy \(A\) chia hết cho 31

\(a)\) Ta có : 

\(\frac{a}{b}< \frac{a+c}{b+c}\)

\(\Leftrightarrow\)\(a\left(b+c\right)< b\left(a+c\right)\)

\(\Leftrightarrow\)\(ab+ac< ab+bc\)

\(\Leftrightarrow\)\(ac< bc\)

\(\Leftrightarrow\)\(a< b\)

Mà \(a< b\) \(\Rightarrow\) \(\frac{a}{b}< 1\)

Vậy ...

Mik xem có bạn nào làm được ko nhé !!!

Bạn nào làm được mik cho 6 k !!!

Mik bít cách giải đó !!

Nhưng đăng lên đây để các bạn cùng giải thôi !!!

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