\(a,\dfrac{53}{57}=\dfrac{53.10}{57.10}=\dfrac{530}{570}=1-\dfrac{40}{570}\\ \dfrac{531}{571}=1-\dfrac{40}{571}\\ Vì:\dfrac{40}{570}>\dfrac{40}{571}\Rightarrow1-\dfrac{40}{570}< 1-\dfrac{40}{571}\\ \Leftrightarrow\dfrac{53}{57}< \dfrac{531}{571}\)

b đâu ạ

a,333^444 < 444^333

B,5^340 > 7^255

\(1.\)

a, \(27^{265}\)và \(81^{199}\)

\(27^{265}=\left(3^3\right)^{265}=3^{795}\)

\(81^{199}=\left(3^4\right)^{199}=3^{796}\)

\(\Rightarrow3^{795}< 3^{796}hay27^{265}< 81^{199}\)

b, \(1024^{15}=\left(2^{10}\right)^{15}=2^{150}\)

\(128^{21}=\left(2^7\right)^{21}=2^{147}\)

\(2^{150}>2^{147}.hay.1024^{15}>128^{21}\)

A<B

a)2^6=8^2

b)5^3<3^5

a) \(2^6\) và \(8^2\)

   \(2^6=\left(2^2\right)^3\)

  \(8^2=\left(2^3\right)^2\)\(=2^6\)

 \(\Rightarrow\) \(2^6=8^2\)

Bài làm

b ) Ta có : 

\(2^{3333}\)= \(\left(2^3\right)^{1111}\)= \(8^{1111}\)

\(3^{2222}\)= \(\left(3^2\right)^{1111}\)= \(9^{1111}\)

Vì \(9^{1111}>8^{1111}\)

nên \(3^{2222}>2^{3333}\)

Bài làm

Ta có: 5³⁴⁰ = 5^68.5 = (5⁶⁸)⁵ = 338813178901720135627329000271856784820556640625⁵

          7²⁵⁵ = 7^51.5 = (7⁵¹)⁵ = 12589255298531885026341962383987545444758743⁵

Mà 12589255298531885026341962383987545444758743 < 338813178901720135627329000271856784820556640625

=> 12589255298531885026341962383987545444758743⁵ < 338813178901720135627329000271856784820556640625⁵ 

Hay 7²⁵⁵ < 5³⁴⁰ 

Vậy 7²⁵⁵ < 5³⁴⁰ 

b) Ta có: 2³³³³ = 2^3.1111 = (2³)¹¹¹¹ = 8¹¹¹¹

               3²²²² = 3^2.1111 = (3²)¹¹¹¹ = 9¹¹¹¹

Mà 8 < 9

=> 8¹¹¹¹ < 9¹¹¹¹ 

Hay 2³³³³ < 3²²²² 

Vậy 2³³³³ < 3²²²² 

# Chúc bạn học tốt #

a: 99^20=9801^10<9999^10

b: 3^500=243^100

5^300=125^300

=>3^500>5^300

\(a,2^{300}=\left(2^3\right)^{100}=8^{100}\)

\(3^{200}=\left(3^2\right)^{100}=9^{100}\)

Vì \(8^{100}< 9^{100}\) nên \(2^{300}< 3^{200}\)

\(b,8^5=32768\)

\(6^6=46656\)

Vì \(32768< 46656\) nên \(8^5< 6^6\)

\(c,3^{450}=\left(3^3\right)^{150}=27^{150}\)

\(5^{300}=\left(5^2\right)^{150}=25^{150}\)

Vì \(27^{150}>25^{150}\) nên \(3^{450}>5^{300}\)

#Ayumu