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![](https://rs.olm.vn/images/avt/0.png?1311)
ta có:
5300= (52)150= 25150
3450= (33)150= 27150
vì 25150< 27150=> 5300< 3450
vậy 5300< 3450
Ta có:\(5^{300}=\left(5^2\right)^{150}=25^{150}\)
\(3^{450}=\left(3^3\right)^{150}=27^{150}\)
Vì \(25^{150}< 27^{150}\) nên \(5^{300}< 3^{450}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
3x24^100=(2x3x4)^100
=3x(3^100)x4^150
xet 4^300-3x24^100=
4^300-3x(3^100)x4^150=
(4^150)(4^150-3x3^100)>
(4^150)(3^150-3x3^100)>
(4^150)(3^100)(3^50-3)>0
==>.....
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta co : 3500 va -5300
=>3500=(35)100=243100 (1)
=>-5300=(-53)100=-125100 (2)
Tu (1) va (2) suy ra 3500>-5300
lik e nhe
3500 và -5300
3500 = ( 3 5 ) 100 = 243100
-5300 = ( -5 3)100 = -125100
do 243 > -125 nên => 243100 > -125100
=> 3500 > -5300
tick nhé
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(-\frac{1}{5}\right)^{300}=-\frac{1^{300}}{5^{300}}=-\frac{1}{5^{300}}\)
\(\left(-\frac{1}{5}\right)^{500}=-\frac{1^{500}}{5^{500}}=-\frac{1}{5^{500}}\)
Ta có :
\(5^{300}< 5^{500}\)
\(\Rightarrow-5^{300}>-5^{500}\)
\(\Rightarrow-\frac{1}{5^{300}}>-\frac{1}{5^{500}}\)
\(\Rightarrow\left(-\frac{1}{5}\right)^{300}>\left(-\frac{1}{5}\right)^{500}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: \(5^{300}=\left(5^3\right)^{100}=125^{100}\)(1)
\(3^{500}=\left(3^5\right)^{100}=243^{100}\)(2)
Từ (1) và (2) suy ra \(5^{300}< 3^{500}\)
\(\Rightarrow\frac{1}{5^{300}}>\frac{1}{3^{500}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
\(\left(\dfrac{-1}{3}\right)^{500}=\left(\dfrac{1}{3}\right)^{500}=\dfrac{1}{3^{500}}=\dfrac{1}{3^{5^{100}}}=\dfrac{1}{243^{100}}\)
\(\left(\dfrac{-1}{5}\right)^{300}=\left(\dfrac{1}{5}\right)^{300}=\dfrac{1}{5^{300}}=\dfrac{1}{5^{3^{100}}}=\dfrac{1}{125^{100}}\)
Vì 243100 > 125100 nên \(\dfrac{1}{243^{100}}\) < \(\dfrac{1}{125^{100}}\). \(\Rightarrow\) \(\left(\dfrac{-1}{3}\right)^{500}\)< \(\left(\dfrac{-1}{5}\right)^{300}\)
Vậy...
![](https://rs.olm.vn/images/avt/0.png?1311)
(-1/5)^300= [(-1/5)^3]^100=(1/125)^100
(-1/3)^500=[(-1/3)^5]^100=(1/243)^100
k mik tròn 45 nhé
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có :
\(-\left(\frac{1}{3}\right)^{500}=-\left(\frac{1}{3}\right)^{5.100}=\) \(-\left(\frac{1}{243}\right)^{100}\)
\(-\left(\frac{1}{5}\right)^{300}=-\left(\frac{1}{5}\right)^{3.100}\) =\(-\left(\frac{1}{125}\right)^{100}\)
Vì \(-\left(\frac{1}{125}\right)< -\left(\frac{1}{243}\right)\)nên \(-\left(\frac{1}{3}\right)^{500}>-\left(\frac{1}{5}\right)^{300}\)
\(5^{300}=\left(5^3\right)^{100}=125^{100}< 243^{100}=\left(3^5\right)^{100}=3^{500}\)
\(5^{300}=\left(5^3\right)^{100}=125^{100}< 243^{100}=\left(3^5\right)^{100}=3^{500}\)