Ta có : \(\frac{2^9}{3^{2010}}:\frac{3^9}{2^{2010}}=\frac{2^{2019}}{3^{2019}}=\left(\frac{2}{3}\right)^{2019}< 1^{2019}=1\)

Vì \(\frac{2^9}{3^{2010}}:\frac{3^9}{2^{2010}}< 1\)

=> \(\frac{2^9}{3^{2010}}< \frac{3^9}{2^{2010}}\)

       Bài làm :

Cách 1:

Ta có :

 \(\frac{2^9}{3^{2010}}\div\frac{3^9}{2^{2010}}=\frac{2^9.2^{2010}}{3^{2010}.3^9}=\frac{2^{2019}}{3^{2019}}=\left(\frac{2}{3}\right)^{2019}< 1\)

 \(\Rightarrow\frac{2^9}{3^{2010}}< \frac{3^9}{2^{2010}}\)

Cách 2 :

Nhận thấy :

• 2⁹ < 3⁹
• 3²⁰¹⁰ > 2²⁰¹⁰

\(\Rightarrow\frac{2^9}{3^{2010}}< \frac{3^9}{2^{2010}}\)

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

\(2^{333}< 3^{222}\)

mình cần cách giải

>

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

Ta có: 2⁶⁰³=(2³)²⁰¹=8²⁰¹; 3⁴⁰²=(3²)²⁰¹=9²⁰¹

Vì 8<9 nên 2⁶⁰³<3⁴⁰²

a) Ta có: \(3^{40}=\left(3^4\right)^{10}=81^{10}\)

              \(5^{30}=\left(5^3\right)^{10}=125^{10}\)

Vì 125 > 81 => \(125^{10}>81^{10}\) => \(3^{40}>5^{30}\)

b) Ta có: \(5^{303}>5^4\) vì 303 > 4

         Mà: \(5^4>2^4\)  vì 5 > 2

=> \(5^{303}>2^4\)

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