![](https://rs.olm.vn/images/avt/0.png?1311)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
125100=53.100=5300
36150=62.150=6300
vì 5<6 nên 5300<6300
125100< 36150
Ta co: 125^100=(125^2)^50=15625^50 36^150=(36^3)50=46650^50 Vi 46650>15625=>46650^50>15625^50=>125^100<36^150 NHO **** NHE
![](https://rs.olm.vn/images/avt/0.png?1311)
2^150=(2^3)^50=8^50
3^100=(3^2)^50=9^50
9^50 > 8^50 = > 3^100 > 2 ^150
**** mik nha
2^150=(2^3)^50=8^50
3^100=(3^2)^50=9^50
9^50 > 8^50 = > 3^100 > 2 ^150
tick mik nha
nhơ sđó
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
+) 2150=(23)50
+) 3100=(32)50
Mà (23)50<(32)<50
=> 2150<3100
Vậy ...
Chúc bạn học tốt
2150 và 3100
2150 = ( 23 ) 50 = 850
3100 = ( 32 ) 50 = 950
Vì 8 < 9
= > 850 < 950
![](https://rs.olm.vn/images/avt/0.png?1311)
\(-\left(-\dfrac{1}{16}\right)^{100}=-\left(-\dfrac{1}{2^4}\right)^{100}=-\left(\dfrac{1}{2^4}\right)^{100}=-\left[\left(\dfrac{1}{2}\right)^4\right]^{100}=-\left(\dfrac{1}{2}\right)^{400}=-\dfrac{1}{2^{400}}\)
\(-\left(-\dfrac{1}{8}\right)^{150}=-\left(-\dfrac{1}{2^3}\right)^{150}=-\left(\dfrac{1}{2^3}\right)^{150}=-\left[\left(\dfrac{1}{2}\right)^3\right]^{150}=-\left(\dfrac{1}{2}\right)^{450}=-\dfrac{1}{2^{450}}\)
\(\dfrac{1}{2^{400}}>\dfrac{1}{2^{450}}\Rightarrow-\dfrac{1}{2^{400}}< -\dfrac{1}{2^{450}}\)
Vậy \(-\left(-\dfrac{1}{6}\right)^{100}< -\left(-\dfrac{1}{8}\right)^{150}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: \(2^{150}=\left(2^3\right)^{50}=8^{50}\)
\(3^{100}=\left(3^2\right)^{50}=9^{50}\)
Vì \(8^{50}< 9^{50}\) nên \(2^{150}< 3^{100}\)
Vậy \(2^{150}< 3^{100}\)
Ta có: 2150 = (23)50 = 850
3100 = (32)50 = 950
Vì 8 < 9 nên 850 < 950
Vậy 2150 < 3100
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
\(\frac{\left(5^4-5^3\right)^3}{125^5}=\frac{\left(5^3\right)^3.\left(5-1\right)^3}{\left(5^3\right)^5}=\frac{5^9.4^3}{5^{15}}=\frac{4^3}{5^6}=\frac{64}{5^6}\) (1)
\(\frac{64}{25^3}=\frac{64}{\left(5^2\right)^3}=\frac{64}{5^6}\) (2)
Từ (1) và (2) =>\(\frac{\left(5^4-5^3\right)^3}{125^5}=\frac{64}{25^3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có:
2150=(23)50=850
3100=(32)100=950
vì 8<9 nên 850<950
hay 2150<3100
Ta có: 125100=(53)100=53.100=5300
36150=(62)150=62.150=6300
Vì 5<6
=>5300<6300
=>125100<36150
\(125^{100}=\left(5^3\right)^{100}=5^{300}\left(1\right)\)
\(36^{150}=\left(6^2\right)^{150}=6^{300}\left(2\right)\)
từ (1) và (2)=>125^100<36^150