2^300 = (2³)^100 = 8^100 
3^200 = (3²)^100 = 9^100 
Vì 8 < 9 nên 8^100 < 9^100 =>2^300 < 3^200.

\(2^{300}=2^{3\times100}=\left(2^3\right)^{100}=8^{100}\)

\(3^{200}=3^{2\times100}=\left(3^2\right)^{100}=9^{100}\)

vì 8^100< 9^100 nên 2^300<3^200

\(2^{50}=\left(2^5\right)^{10}=32^{10}\)

\(5^{20}=\left(5^2\right)^{10}=25^{10}\)

Suy ra: 2⁵⁰ > 5²⁰

b)

\(9^{200}=\left(9^2\right)^{100}=81^{100}\)

Suy ra: 99¹⁰⁰ > 81¹⁰⁰

\(5^{202}=\left(5^2\right)^{101}=25^{101}\)

\(2^{505}=\left(2^5\right)^{101}=32^{101}\)

Suy ra: 5²⁰² < 2⁵⁰⁵

a) 5²⁰⁰ = (5²)¹⁰⁰ = 25¹⁰⁰

3⁴⁵³= 3⁴⁰⁰ x 3⁵³ = ( 3⁴)¹⁰⁰ x 3⁵³ = 81¹⁰⁰ x 3⁵³

Ta thấy 81¹⁰⁰ > 25¹⁰⁰ => 81¹⁰⁰ x 3⁵³ > 25¹⁰⁰

Vậy 3⁴⁵³ > 5²⁰⁰ 

b) 2¹⁶⁴= 2¹⁶⁰ x 2⁴ = (2⁴)⁴⁰ x2⁴ = 16⁴⁰ x 2⁴

Ta thấy: 16⁴⁰ > 13⁴⁰ =>  16⁴⁰ x 2⁴ > 13⁴⁰

Vậy 2¹⁶⁴ > 13⁴⁰

Nhớ          k mik nha

\(2^x=4^3=\left(2^2\right)^3=2^6\Rightarrow x=6.\)

Trả lời

4¹⁰⁰=2²⁰⁰

2²⁰²

Vậy 2²⁰⁰ < 2²⁰² hay 4¹⁰⁰ < 2²⁰²

3⁰ và 5⁸

3⁰ < 5⁸

a, \(4^{100}=\left(2^2\right)^{100}=2^{200}< 2^{202}\)

\(\Rightarrow\text{ }4^{100}< 2^{202}\)

b, \(3^0=1< 5^8\)

\(3^0< 5^8\)

c, \(\left(0,6\right)^0=1\)

\(\left(-0,9\right)^6=\left(0,9\right)^6\)

\(\Rightarrow\text{ }\left(0,6\right)^0< \left(-0,9\right)^6\)

d, 

e, \(8^{12}=\left(2^3\right)^{12}=2^{36}=2^{16}\cdot2^{20}=2^{16}\cdot\left(2^4\right)^5=2^{16}\cdot16^5\)

\(12^8=\left(2^2\cdot3\right)^8=2^{16}\cdot3^8=2^{16}\cdot\left(3^2\right)^4=2^{16}\cdot9^4\)

Vì \(2^{16}\cdot16^5>2^{16}\cdot9^4\text{ }\Rightarrow\text{ }8^{12}>12^8\)

a,3¹² và 5⁸

Ta có:3¹²=(3³)⁴=27⁴

5⁸=(5²)⁴=25⁴

Vì 27⁴>25⁴ nên 3¹²>5⁸

b,(0,6)⁹ và (0,9)⁶

Ta có:(0,9)⁶>(0,6)⁶ mà (0,6)⁶>(0,6)⁹

\(\Rightarrow\)(0,6)⁹<(0,9)⁶

c,5²⁰⁰⁰ và 10¹⁰⁰⁰

Ta có:5²⁰⁰⁰=(5²)¹⁰⁰⁰=25¹⁰⁰⁰>10¹⁰⁰⁰

\(\Rightarrow\)5²⁰⁰⁰>10¹⁰⁰⁰

d,?????

2³⁰⁰<3²²⁵

\(2^{300}=\left(2^4\right)^{75}=16^{75}\)

\(3^{225}=\left(3^3\right)^{75}=27^{75}\)

mà 16<27

nên \(2^{300}< 3^{225}\)