\(3^{200}=9^{100}>4^{100}\\ 5^{200}=25^{100}< 64^{100}=4^{300}\\ 6^{50}=36^{25}>7^{25}\\ 8^{40}=64^{20}>10^{20}\\ 16^{20}=256^{10}>32^{10}\)

tick mik nha!!

3200=9100>41005200=25100<64100=4300650=3625>725840=6420>10201620=25610>3210

a: \(3^{200}=\left(3^2\right)^{100}=9^{100}>4^{100}\)

b: \(5^{200}=\left(5^2\right)^{100}=25^{100}\)

\(4^{300}=\left(4^3\right)^{100}=64^{100}\)

mà 25<64

nên \(5^{200}< 4^{300}\)

c: \(6^{50}=\left(6^2\right)^{25}=36^{25}>7^{25}\)

a: \(2^{333}=8^{111}< 9^{111}=3^{222}\)

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

Ta có : 

9¹⁰⁰⁵ = ( 3² )¹⁰⁰⁵ = 3²⁰¹⁰ < 3²⁰⁰⁹

nên 3²⁰⁰⁹ < 9¹⁰⁰⁵

Ta có 3^2009=3^2008.3=(3^2)^1004.3=9^1004.3

9^1005=9^1004.9

Vì 9^1004.9>9^1004.3 nên 9^1005>3^2009

Ta có :

\(9^{1005}=\left(3^2\right)^{1005}=3^{2010}\)

Vì \(3^{2009}< 3^{2010}\)( 2009 < 2010 )

\(\Rightarrow\)\(3^{2009}< 9^{1005}\)

Vậy bạn tự kết luận 

Ta có:

9¹⁰⁰⁵ = (3²)¹⁰⁰⁵ = 3²⁰¹⁰

Mà 3²⁰¹⁰ > 3²⁰⁰⁹ ( 2010 > 2009 )

=> 9¹⁰⁰⁵ > 3²⁰⁰⁹

Ta có :

\(3^{2009}\left(1\right)\)

\(9^{1005}=\left(3^2\right)^{1005}=3^{2010}\)\(\left(2\right)\)

Từ \(\left(1\right)+\left(2\right)\Leftrightarrow3^{2009}< 3^{1005}\)

Ta có: \(3^{2009}\) ( giữ nguyên )

\(9^{1005}=\left(3^2\right)^{1005}=3^{2010}\)

Vì 2009 < 2010 nên \(3^{2009}< 3^{2010}\)

Vậy \(3^{2009}\) < \(9^{1005}\)

ta có 9¹⁰⁰⁵=(3²)¹⁰⁰⁵=3²⁰¹⁰

vì 2009<2010

=> 3²⁰⁰⁹< 3²⁰¹⁰

hay 3²⁰⁰⁹ <9¹⁰⁰⁵

Ta có : \(9^{1005}=\left(3^2\right)^{1005}=3^{2010}\)

Vì : 2009 < 2010 nên \(3^{2009< }3^{2010}\)

Vậy \(3^{2009}< 9^{1005}\)

a.ta có: \(3^{2009}\)

\(9^{1005}\)= \(\left(3^2\right)^{1005}\) =\(3^{2010}\)

*Vì 2010> 2009 =>\(3^{2009}\) < \(3^{2010}\)

Vậy \(3^{2009}\) < \(9^{1005}\).

\(3\sqrt{3}-2\sqrt{2}=\sqrt{27}-\sqrt{8}>\sqrt{25}-\sqrt{9}=5-3\)

\(\Rightarrow3\sqrt{3}-2\sqrt{2}>2\)