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\(2^{333}=\left(2^3\right)^{111}=8^{111}\\ 3^{222}=\left(3^2\right)^{111}=9^{111}\)
VÌ\(8^{111}< 9^{111}\Rightarrow2^{333}< 3^{222}\)
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nguyenthanhtung NHỚ K
\(2^{333}=\left(2^3\right)^{111}=8^{111}\)
\(3^{222}=\left(3^2\right)^{111}=9^{111}\)
VÌ \(8^{111}< 9^{111}\)NÊN \(2^{333}< 3^{222}\)
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`@` `\text {Ans}`
`\downarrow`
Ta có:
\(5^{333}=\left(5^3\right)^{111}=125^{111}\)
\(11^{222}=\left(11^2\right)^{111}=121^{111}\)
Vì `125 > 121 =>`\(125^{111}>121^{111}\)
`=>`\(5^{333}>11^{222}\)
Vậy, \(5^{333}>11^{222}\)
_____
`@` So sánh lũy thừa cùng cơ số:
Nếu `m > n =>`\(a^m>a^n\left(m,n\ne0,a>1\right)\)
`@` So sánh lũy thừa cùng số mũ:
Nếu `a > b =>`\(a^m>b^m\left(a,b>1,m\ne0\right)\)
`@` `\text {Kaizuu lv uuu}`
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Ta có:
222^555=(2^5.111^5)^111
555^222=(5^2.111^2)^111
Mà 2^5.111^5=32.111^5 > 25.111^2=5^2.111^2
=> 222^555>555^222
222^555=(111^2)^555=111^1110
555^222=(111^5)^222=111^1110
Vi 1110=1110 suy ra 111^1110=111^1110
suy ra 222^555=555^222
Vay.......
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:334>330=(33)10=2710.
. 520=(52)10=2510.
Vì 27>25=>2710>2510=>330>520.
Mà 334>330.
Nên 334>520.
![](https://rs.olm.vn/images/avt/0.png?1311)
2^333 = (2^3)^111 = 8^111
3^222 = (3^2)^111 = 9 ^111
Vì 8< 9 => 8^111 < 9^111 => 2^333 < 3^222
Ta có: 2^333 = (2^3)^111 = 8^111
3^222 = (3^2)^111 = 9^111
Vì 8^111 < 9^111 nên 2^333 < 3^222
ta có: 2333 = (23)111 = 8111
3222 =(32)111 = 9111
=> ....
TC \(2^{333}=\)\(2^{3.111}\)\(\left(2^3\right)^{111}=8^{111}\)
LC \(3^{222}=3^{2.111}=\left(3^2\right)^{111}=9^{111}\)
MÀ 8<9
\(\Rightarrow8^{111}< 9^{111}\)
\(hay\)\(2^{333}< 3^{222}\)