a)\(5^{23}=5.5^{22}\)

\(6.5^{22}\)

Vì \(5.5^{22}< 6.5^{22}\Rightarrow5^{23}< 6.5^{22}\)

b)\(abc-cba=\left(100a+10b+c\right)-\left(100c+10b+a\right)=100a+10b+c-100c-10b-a=\left(100a-a\right)+\left(10b-10b\right)+\left(100c-c\right)=99a+0+99c⋮99\Rightarrow abc-cba⋮99\)

Bài 2:

a)\(ab+ba⋮11=10a+b+10b+a=11a+11b⋮11\Rightarrow ab+ba⋮11\)

7x - 2 + 5x = 22

7x + 5x = 22 + 2

12x = 24

x = 24 : 12

x = 2

c)\(81^7-27^9-9^{13}=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}\)

\(=3^{28}-3^{27}-3^{26}=\left(3^{24}.3^4\right)-\left(3^{24}.3^3\right)-\left(3^{24}.3^2\right)\)

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

\(=3^{24}.45\Rightarrow81^7-27^9-9^{13}⋮45\)

b)\(7^6+7^5-7^4=\left(7^4.7^2\right)+\left(7^4.7\right)-7^4\)

\(=7^4.7^2+7^4.7-7^4\)\(=7^4.\left(7^2+7-1\right)\)

\(=7^4.55\Rightarrow7^6+7^5-7^4⋮11\)

Bài 2:

a)\(8^{10}-8^9-8^8=\left(8^8.8^2\right)-\left(8^8.8\right)-8^8\)

\(=8^8.8^2-8^8.8-8^8=8^8.\left(8^2-8-1\right)\)

\(=8^8.55\Rightarrow8^{10}-8^9-8^8⋮55\)

d)\(2.x-138=2^3.3^2\)

\(2.x-138=8.9\)

\(2.x-138=72\)

\(2.x=72+138\)

\(2.x=210\)

\(x=210:2\)

\(x=105\)

c)\(10+2.x=4^5:4^3\)

\(10+2.x=4^{5-3}\)

\(10+2.x=4^2=16\)

\(2.x=16-10\)

\(2.x=6\)

\(x=6:2\)

\(x=3\)

b)\(70-5.\left(x-3\right)=45\)

\(5.\left(x-3\right)=70-45\)

\(5.\left(x-3\right)=35\)

\(x-3=35:5\)

\(x-3=7\)

\(x=7+3\)

\(x=10\)