1024⁹ = (2¹⁰)⁹ = 2⁹⁰

Có 2¹⁰⁰ > 2⁹⁰

=> 2¹⁰⁰ > 1024⁹

Ta có: 1024⁹=(2¹⁰)⁹=2⁹⁰

Vì 2¹⁰⁰>2⁹⁰ nên 2¹⁰⁰>1024⁹

1024^9=2^90

2^100>2^90

=> 2^100>1024^9

Nho tick nha

> kho giai thich lm ;-;

99^100 lớn hơn

10²⁰⁰ = (11²)¹⁰⁰ = 121¹⁰⁰

Vì 121 > 99 nên 121¹⁰⁰ > 99¹⁰⁰

=> 10²⁰⁰ > 99¹⁰⁰

\(10^{200}=10^{\left(100.2\right)}=\left(10^2\right)^{100}=100^{100}\)

Vì \(100^{100}>99^{100}\)

nên \(10^{200}>99^{100}\)

a) Ta có: \(A=1+2013+2013^2+...+2013^{99}\)

   \(2013A=2013+2013^2+2013^3+...+2013^{100}\)

\(2013A-A=2013^{100}-1\)

Hay \(2012A=2013^{100}-1\)

\(\Rightarrow2012A=2013^{100}-1< 2013^{100}=B\)

\(\Rightarrow A< B\)

_Học tốt_

hdjshfkjdksj

a) \(\frac{999}{10000}=\frac{99,9}{1000}>\frac{99}{100}\)

=> kết luận

b)  \(1-\frac{97}{99}=\frac{2}{99}>1-\frac{98}{100}=\frac{2}{100}\)

\(\Rightarrow\frac{97}{99}< \frac{98}{100}\)

=> kết luận

Ta có:\(2^{600}=\left(2^6\right)^{100}=64^{100}\)

\(7^{200^{ }^{ }}=\left(7^2\right)^{100}=49^{100}\)

Vì \(64^{100}>49^{100}\)

Suy ra: \(2^{600}>7^{200}\)

Ta có: \(2^{600}=\left(2^6\right)^{100}=64^{100}\)

\(7^{200}=\left(7^2\right)^{100}=49^{100}\)

Vì \(64^{100}>49^{100}\)

Suy ra: \(2^{600}>7^{200}\)

Ta có:

2⁶⁰⁰ = 2^{3 . 200} = (2³)²⁰⁰ = 8²⁰⁰

Mà 8²⁰⁰ > 7²⁰⁰

Nên 2⁶⁰⁰ > 7²⁰⁰.