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a) Ta có: \(3^{40}=\left(3^4\right)^{10}=81^{10}\)
\(5^{30}=\left(5^3\right)^{10}=125^{10}\)
Vì 125 > 81 => \(125^{10}>81^{10}\) => \(3^{40}>5^{30}\)
b) Ta có: \(5^{303}>5^4\) vì 303 > 4
Mà: \(5^4>2^4\) vì 5 > 2
=> \(5^{303}>2^4\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Ta có :
\(27^{27}>27^{26}=\left(27^2\right)^{13}=729^{13}>243^{13}\)
\(\Rightarrow27^{27}>243^{13}\)
\(\Rightarrow-27^{27}< -243^{13}\)
\(\Rightarrow\left(-27\right)^{27}< \left(-243\right)^{13}\)
b) \(\left(\dfrac{1}{8}\right)^{25}>\left(\dfrac{1}{8}\right)^{26}=\left(\dfrac{1}{8^2}\right)^{13}=\left(\dfrac{1}{64}\right)^{13}>\left(\dfrac{1}{128}\right)^{13}\)
\(\Rightarrow\left(\dfrac{1}{8}\right)^{25}>\left(\dfrac{1}{128}\right)^{13}\)
\(\Rightarrow\left(-\dfrac{1}{8}\right)^{25}< \left(-\dfrac{1}{128}\right)^{13}\)
c) \(4^{50}=\left(4^5\right)^{10}=1024^{10}\)
\(8^{30}=\left(8^3\right)^{10}=512^{10}< 1024^{10}\)
\(\Rightarrow4^{50}>8^{30}\)
d) \(\left(\dfrac{1}{9}\right)^{17}< \left(\dfrac{1}{9}\right)^{12}< \left(\dfrac{1}{27}\right)^{12}\)
\(\Rightarrow\left(\dfrac{1}{9}\right)^{17}< \left(\dfrac{1}{27}\right)^{12}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2^{50}=\left(2^5\right)^{10}=32^{10}\)
\(5^{20}=\left(5^2\right)^{10}=25^{10}\)
Suy ra: 250 > 520
b)
\(9^{200}=\left(9^2\right)^{100}=81^{100}\)
Suy ra: 99100 > 81100
![](https://rs.olm.vn/images/avt/0.png?1311)
\(25^{15}=5^{30}\)
\(8^{10}\cdot3^{30}=6^{30}\)
Do đó: \(25^{15}< 8^{10}\cdot3^{30}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1,1020và 9010
ta có:+,1020=(102)10=10010
+,9010=9010
vì 10010>9010=>1020>9010
2,(1/16)10 và (1/2)50
ta có:+, (1/16)10=(1/16)10
+,(1/2)50=(1/25)10=(1/32)10
vì (1/16)10>(1/32)10=>(1/16)10>(1/2)50
k mik nhé
\(a,\) \(10^{20}=10^{10+10}=10^{10}.10^{10}\)
\(90^{10}=9^{10}.10^{10}\)
Vì \(10^{10}.10^{10}>9^{10}.10^{10}\)
\(\Rightarrow10^{20}>90^{10}\)
Vậy \(10^{20}>90^{10}\)
\(b,\)\(\left(\frac{1}{16}\right)^{10}=\frac{1^{10}}{16^{10}}=\frac{1}{\left(4^2\right)^{10}}=\frac{1}{4^{20}}\)
\(\left(\frac{1}{2}\right)^{50}=\frac{1^{50}}{2^{50}}=\frac{1}{\left(2^2\right)^{25}}=\frac{1}{4^{25}}\)
Vì \(\frac{1}{4^{20}}>\frac{1}{4^{25}}\)
\(\Rightarrow\left(\frac{1}{16}\right)^{10}>\left(\frac{1}{2}\right)^{50}\)
Vậy \(\left(\frac{1}{16}\right)^{10}>\left(\frac{1}{2}\right)^{50}\)
~~~~~~~~~~Hok tốt~~~~~~~~~~~
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có : 430 = (22)30 = 22.30 = 260
Lại có : 820 = (23)20 = 23.20 = 260
Vì 260 = 260
=> 430 = 820
Ta có:
\(\left(-5\right)^{30}=\left(-5^3\right)^{10}=\left(-125\right)^{10}=125^{10}\)
\(\left(-3\right)^{50}=\left(-3^5\right)^{10}=\left(-81\right)^{10}=81^{10}\)
Vì \(125^{10}>81^{10}\)
⇒\(\left(-5\right)^{30}>\left(-3\right)^{50}\)
\(\left(-5\right)^{30}\) và \(\left(-3\right)^{50}\)
Ta có: \(\left(-5\right)^{30}=\left[\left(-5\right)^3\right]^{10}=\left(-125\right)^{10}\)
\(\left(-3\right)^{50}=\left[\left(-3\right)^5\right]^{10}=\left(-243\right)^{10}\)
Vì \(\left(-125\right)^{10}< \left(-243\right)^{10}\) nên \(\left(-5\right)^{30}< \left(-3\right)^{50}\)