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a) 19920 < 20020
200015 < 200315
ta có : 20020 = ( 8 . 25 ) 20 = ( 23 . 52 )20 = 260 . 540
200015 = ( 2 .103 ) 15 = ( 24 . 53 ) 15 = 260 . 545
Vì 40 < 45 nên 260 . 540 < 260 . 545 hay 19920 < 200315
b) 5217 và 11972
ta có : 5217 > 5216 = 12572 > 11972
Vì 5217 > 5216 hoặc 12572 > 11972
nên 5217 > 11972
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
199^20 < 200^20 = 200^15.200^5
2003^15 > 2000^15 = 200^15.10615 = 200^15.(10^3)^5 = 200^15.1000^5
Vì 199^20 < 200^15.200^5 < 200^15.1000^5 < 2003^15
=> 199^20 < 2003^15
![](https://rs.olm.vn/images/avt/0.png?1311)
+ Ta có \(199^{20}< 216^{20}=\left(6^3\right)^{20}=6^{60}\)
+ Ta có \(2003^{15}>1296^{15}=\left(6^4\right)^{15}=6^{60}\)
=> \(199^{20}< 2003^{15}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) 2003^15 > 2000^15 = (2.10^3)^15 = 2^15.10^45
199^20 < 200^20 = (2.10^2)^20 = 2^20.10^40 =2^15.2^5.10^40 <2^15.10^40.100 =2^15.10^42
Vậy 199^20 < 2003^15
b) 3^99 > 11^21
vì
3^99 = (3³³)³
11^21 = (11^7)³
Còn số mũ giờ so sánh 3³³ và 11^7
3³³ = (3^4)^7 * 3^5
mà 3^4 > 11
==> 3^99 > 11^21
![](https://rs.olm.vn/images/avt/0.png?1311)
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![](https://rs.olm.vn/images/avt/0.png?1311)
6255 = (54)5 = 54x5 = 520
1257 = (53)7 = 53x7 = 521
Vì 520 < 521 nên 6255 < 1257
![](https://rs.olm.vn/images/avt/0.png?1311)
b)Ta có:
\(3^{99}>3^{93}=\left(3^3\right)^{21}=27^{21}\)
Vì \(27^{21}>11^{21}\) nên \(3^{99}>27^{21}>11^{21}\) hay \(3^{99}>11^{21}\)
a) Ta có:
19920 < 20020 = 20015.2005
200315 > 200015 = 20015.1015 = 20015.(103)5 = 20015.10005
Vì 19920 < 20015.2005 < 20015.10005 < 200315
=> 19920 < 200315
b) Ta có:
399 = (33)33 = 2733 > 1121
=> 399 > 1121