(2⁵)⁸.4¹⁰

=2⁴⁰.(2²)¹⁰

=2⁴⁰.2²⁰

=2⁶⁰

  2⁰.4^10..8¹².10

=2⁰.(2²)¹⁰.(2³)¹².10

=2⁰.2²⁰.2³⁶.(2³+ 2)

=2⁵⁹+ 2

nên A > B

Tính
A=2⁴⁰.4¹⁰
B=1.4¹⁰.16=4¹⁰.16=4¹⁰.2⁴
Ta thấy 2⁴⁰>2⁴ 
=> A>B

Xét A=(2⁵)⁸.4¹⁰=2⁴⁰.2²⁰=2⁶⁰

B=2⁰.4¹⁰.16=2⁰.2²⁰.2⁴=2²⁴

Vì 2⁶⁰>2²⁴=>A>B

\(A=\frac{1\cdot2+2\cdot4+3\cdot6+4\cdot8+5\cdot10}{3\cdot4+6\cdot8+9\cdot12+12\cdot16+15\cdot20}\)

\(=>A=\frac{1\cdot2+4\cdot1\cdot2+9\cdot1\cdot2+16\cdot1\cdot2+25\cdot1\cdot2}{3\cdot4+4\cdot3\cdot4+9\cdot3\cdot4+16\cdot3\cdot4+25\cdot3\cdot4}\)

\(=>A=\frac{\left(1+4+9+16+25\right)\cdot1\cdot2}{\left(1+4+9+16+25\right)\cdot3\cdot4}=\frac{1}{6}=\frac{111111}{666666}\)

Mà \(\frac{111111}{666666}< \frac{111111}{666665}\)

\(=>A< B\)

A và B đều có thừa số là\(4^{10}\) nên triệt tiêu cho nhau.

\(2^0\) = 1 nên không tính

8=\(2^3\)nên \(8^{12}\)=\(2^{36}\)và 16=\(2^4\)nên \(2^{36}\).\(2^4\)=\(2^{40}\)

\(\left(2^5\right)^8\)=\(2^{5.8}\)=\(2^{40}\)

Nên A=B

a)   Ta có: 

+) \(\frac{10^8}{10^7}\)-1=  10^8-7-1=10-1=9 ₍₁₎

+) \(\frac{10^7}{10^6}\)-1=  10^7-6-1=10-1=9 ₍₂₎

Từ (1) và (2) => \(\frac{10^8}{10^7}\)-1=\(\frac{10^7}{10^6}\)-1

Vậy..

a>b vì ...

Bài làm:

Ta có: \(A=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+\frac{1}{7}-\frac{1}{8}+\frac{1}{9}-\frac{1}{10}\)

\(A=\left(1+\frac{1}{3}+...+\frac{1}{9}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{10}\right)\)

\(A=\left[\left(1+\frac{1}{3}+...+\frac{1}{9}\right)+\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{10}\right)\right]-\left[\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{10}\right)+\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{10}\right)\right]\)

\(A=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{10}\right)=B\)

Vậy A = B