bạn vào câu hỏi tương tự nha, có đấy ! nếu thấy đúng thì tick nha!

3²¹>2³¹

\(3^{39}< 11^{21}\)

\(31^{31}>17^{39}\)

đúng thì tc nha

a) Ta có: \(3^{450}=3^{3.150}=\left(3^3\right)^{150}=27^{150}\)

\(5^{300}=5^{2.150}=\left(5^2\right)^{150}=25^{150}\)

Vì 27>25 \(\Rightarrow3^{450}>5^{300}\)

b) \(2^{31}=2.2^{30}=2.\left(2^3\right)^{10}=2.8^{10}\)

\(3^{21}=3.3^{20}=3.\left(3^2\right)^{10}=3.9^{10}\)

Vì \(2.8^{10}< 3.9^{10}\Rightarrow2^{31}< 3^{21}\)

\(\)

a)\(3^{450}=\left(3^3\right)^{150}=27^{150};5^{300}=\left(5^2\right)^{150}=25^{150}\)

27¹⁵⁰>25¹⁵⁰ => 3⁴⁵⁰>5³⁰⁰

b)\(2^{31}=2.2^{30}=2.\left(2^3\right)^{10}=2.8^{10};3^{21}=3.3^{20}=3.\left(3^2\right)^{10}=3.9^{10}\)

2<3;8¹⁰<9¹⁰ => 2.8¹⁰<3.9¹⁰ => 2³¹<3²¹

a) 3^500=(3^5)^100=243^100; 7^300=(7^3)^100=343^100

Vì 243<343 nên 3^500<7^300

k nha

a) UCLN(500,300) là 100

500=100x5

300=100x3

3^500=(3x3x3x3x3)^100=243^100

7^300=(7x7x7)^100=343^100

vì 243^100<343^100 nên 3^500<7^300

bạn làm tương tự với những bài còn lại nha

\(10^{30}\)và \(2^{100}\)

\(10^{30}=\left(10^3\right)^{10}=1000^{10}\)

\(2^{100}=\left(2^{10}\right)^{10}=1024^{10}\)

Vì .....

Vây..

tương tự

a) Có \(3^{125}=3^{124}.3=\left(3^4\right)^{31}.3=81^{31}.3\)
\(4^{93}=\left(4^3\right)^{31}=64^{31}\)
Vì \(81^{31}>64^{31}\Rightarrow81^{31}.3>64^{31}\)
=) \(3^{125}>4^{93}\)
b) Có \(A=\frac{-7}{10^{2005}}+\frac{-15}{10^{2006}}=\frac{-7}{10^{2005}}+\frac{-7}{10^{2006}}+\frac{-8}{10^{2006}}\)
\(B=\frac{-15}{10^{2005}}+\frac{-7}{10^{2006}}=\frac{-7}{10^{2005}}+\frac{-8}{10^{2005}}+\frac{-7}{10^{2006}}\)
Vì \(\frac{-7}{10^{2005}}=\frac{-7}{10^{2005}},\frac{-7}{10^{2006}}=\frac{-7}{10^{2006}},\frac{-8}{10^{2006}}>\frac{-8}{10^{2005}}\)
=) \(\frac{-7}{10^{2005}}+\frac{-7}{10^{2006}}+\frac{-8}{10^{2006}}>\frac{-7}{10^{2005}}+\frac{-8}{10^{2005}}+\frac{-7}{10^{2006}}\)
=) A > B 

a) Ta có: 3¹²⁴= (3⁴)³¹= 81³¹

4⁹³= (4³)³¹= 64 ³¹

Do 81³¹ >  64 ³¹ => 3¹²⁴ < 4⁹³ 

Mà 3¹²⁴< 3¹²⁵ => 3¹²⁵ > 4⁹³ 

333⁴⁴⁴ và 444³³³

ta có : 333⁴⁴⁴ = ( 333⁴ )¹¹¹ =12296370321¹¹¹

444³³³ = ( 444³ )¹¹¹ =  87528384¹¹¹

^vì 12296370321 >  87528384

=> 333⁴⁴⁴ > 444³³³

Bài 1:

333^444 = (333^4)^111

444^333 = (444^3)^111

333^4 = 3^4.111^4 = 81.111^4

444^3 = 4^3.111^3 = 64.111^3 < 81.111^4

444^3< 333^4

(333^4)^111 > (444^3)^111

333^444 > 444^333