so sánh \(^{2^{189}}\) và \(^{3^{126}}\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Do 2189 = 23.63 = (23)63 = 863
3126 = 32.63 = (32)63 = 963
Nên 863 < 963=>2189 < 3126.
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có\(\frac{3^7.9^{10}}{27^8}\)
= > \(\frac{3^7.9^2.9^8}{\left(3.9\right)^8}\)
=>\(\frac{3^7.9^2.9^8}{3^8.9^8}\)
=>\(\frac{3^7.9^2}{3.3^7}\)
=>
=> \(\frac{9^2}{3}\)
=> \(\frac{\left(3.3\right)^2}{3}\)
=>\(\frac{3^2.3^2}{3}\)
=\(\frac{3.3.3^2}{3}\)
= 3 . 3^2
= 3^3
= 27
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: 2189 = (23)63 = 863
3126 = (32)63 = 963
Vì 8 < 9 => 863 < 963 => 2189 < 3126
\(2^{189}=\left(2^9\right)^{21}=512^{21}\)
\(3^{126}=\left(3^6\right)^{21}=729^{21}\)
Vì \(512^{21}< 729^{21}\Rightarrow2^{189}< 3^{126}\)
Vậy \(2^{189}< 3^{126}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) 189 : 3 x 8 > 189 : 9 x 8
b) 25 x 17 > 27 x 15
k mk nha
![](https://rs.olm.vn/images/avt/0.png?1311)
2441=(27)63=12863
5189=(53)63=12563
Vì 128 > 125 => 12863 > 12563 => 2441 > 5189
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{90}{126}=\dfrac{5}{7}\)
\(\Rightarrow\dfrac{90}{126}< \dfrac{6}{7}\) (Vì \(\dfrac{5}{7}< \dfrac{6}{7}\))
\(\dfrac{35}{49}=\dfrac{5}{7}\)
\(\Rightarrow\dfrac{90}{126}=\dfrac{35}{49}\) (Vì \(\dfrac{5}{7}=\dfrac{5}{7}\))