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a.
\(3^{200}=\left(3^2\right)^{100}=9^{100}>8^{100}=\left(2^3\right)^{100}=2^{300}\)
Vậy \(3^{200}>2^{300}\)
b.
\(5^{200}=\left(5^2\right)^{100}=25^{100}< 32^{100}=\left(2^5\right)^{100}=2^{500}\)
Vậy \(5^{200}< 2^{500}\)
Ta có : \(3^{200}=3^{2.100}=\left(3^2\right)^{100}=9^{100}\)
\(2^{300}=2^{3.100}=\left(2^3\right)^{100}=8^{100}\)
\(\Rightarrow9^{100}>8^{100}\)
\(\Rightarrow3^{200}>2^{300}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2^{300}=\left(2^3\right)^{100}=8^{100}\\ 3^{200}=\left(3^2\right)^{100}=9^{100}\\ Vì:8^{100}< 9^{100}\Rightarrow2^{300}< 3^{200}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2^{300}=\left(2^3\right)^{100}=8^{100}\)
\(3^{200}=\left(3^2\right)^{100}=9^{100}>8^{100}\)
\(\Rightarrow2^{300}< 3^{200}\)
`@` `\text {Ans}`
`\downarrow`
Ta có:
\(2^{300}=\left(2^3\right)^{100}=8^{100}\)
\(3^{200}=\left(3^2\right)^{100}=9^{100}\)
Vì `8 < 9 \Rightarrow `\(8^{100}< 9^{100}\)
`\Rightarrow `\(2^{300}< 3^{200}\)
___
`@` So sánh `2` lũy thừa cùng số mũ:
`a^m > b^m` khi `a > b.`
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2^{300}=\left(2^3\right)^{100}=8^{100}\)
\(3^{200}=\left(3^2\right)^{100}=9^{100}\)
mà \(8^{100}< 9^{100}\left(8< 9\right)\)
nên \(2^{300}< 3^{200}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
3200 = 32.100 = 9100 (1)
2300 = 23.100 = 8100 (2)
Từ (1) và(2) ta có: 3200>2300
3200 = 32.100 = (32)100 = 9100
2300 = 23.100 = (23)100 = 8100
9100 > 8100 ( vì 9 > 8 ) nên 3200 > 2300.
![](https://rs.olm.vn/images/avt/0.png?1311)
2^300=(2^3)^100=8^100
3^200=(3^2)^100=9^100
Vì 9>8 =>9^100>8^100 =>2^300<3^200
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có :
2300=(23)100=8100
3200=(32)100=9100
vì 8100<9100 nên 2300<3200
2^300=(2^3)^100=8^100
3^200=(3^2)^100=9^100
vi 8^100<9^100 nen 2^300<3^200
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
\(2^{300}=\left(2^3\right)^{100}=8^{100}\)
\(3^{200}=\left(3^2\right)^{100}=9^{100}\)
\(\Rightarrow3^{200}>2^{300}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
< nhé!
Ta có 2^300=2^(3.100)=8^100
3^200=3^(2.100)=9^100
Vì 8<9=> 2^300<3^200
QUÁ DỄ: 2300 = (23)100 = 8100
3200 = (32)100 = 9100
==> 2300 < 3200
2^306=(23)^102=6102
3^200=(32)^200=6400
vậy ta điền dấu <
ta có : 2 ^306 < 2^300 = 8^100 <9^100= 3^200
=> 2^306<3^200