So sánh 27^45 và 243^27
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(-27\right)^{27}=\left(-3\right)^{3^{27}}=\left(-3\right)^{81}\)
\(\left(-243\right)^{13}=\left(-3\right)^{5^{13}}=\left(-3\right)^{65}\)
\(\Rightarrow\left(-27\right)^{27}< \left(-243^{13}\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(\frac{1}{27}\right)^{10}\&\left(\frac{1}{243}\right)^7\)
\(\left(\frac{1}{27}\right)^{10}=\left(\frac{1}{3^3}\right)^{10}=\frac{1}{3^{30}}\)
\(\left(\frac{1}{243}\right)^7=\left(\frac{1}{3^5}\right)^7=\frac{1}{3^{35}}\)
Vậy \(\left(\frac{1}{27}\right)^{10}>\left(\frac{1}{243}\right)^7\)
Ta có :
\(\left(\frac{1}{27}\right)^{10}=\left(\frac{1}{3^3}\right)^{10}=\frac{1}{3^{30}}\)
\(\left(\frac{1}{243}\right)^7=\left(\frac{1}{3^5}\right)^7=\frac{1}{3^{35}}\)
Do : \(\frac{1}{3^{30}}>\frac{1}{3^{35}}\left(3^{30}< 3^{35}\right)\)
\(\Rightarrow\left(\frac{1}{27}\right)^{10}>\left(\frac{1}{243}\right)^7\)
![](https://rs.olm.vn/images/avt/0.png?1311)
2987.(-1974).(+243).0 Với 0
=-5896338.243.0
=1432810134.0
=0 (ĐPCM)
(-12).(-45):(-27) Với |-1|
=540:(-27)
=-20 < |-1|
=> (-12).(-45):(-27) < |-1|
![](https://rs.olm.vn/images/avt/0.png?1311)
\(243^5=\left(3^5\right)^5=3^{25}\)
\(3.27^8=3.\left(3^3\right)^8=3.3^{24}=3^{25}\)
Vậy\(243^5=3.27^8\)
![](https://rs.olm.vn/images/avt/0.png?1311)
27^5 = (3^3)^5 = 3^3.5 = 3^15
243^3 = (3^5)^3 = 3^5.3 = 3^15
Vậy 27^5 = 243^3
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: 2435=(35)5=35.5=325
3.278=3.(33)8=3.33.8=325
=>325=325
Vậy 2435=3.278
2435 = (35)5 = 325
3 . 278 = 3 . (33)8 = 325
=> 2435 = 3 . 278
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Có:2437=(35)7=335
910x275=(32)10x(33)10=320x330=350
=>..
Ta có:910 = (32)10 =320
275 = (33)5 =315
2437 =(35)7=335
910+275=320+315=335
Mà 335=335
Vậy 2437=910+275
![](https://rs.olm.vn/images/avt/0.png?1311)
275=(3.3.3)5=315
2433=(3.3.3.3.3)3=315
Vậy suy ra 275=2433
\(27^{45}=\left(3^3\right)^{45}=3^{135}\\ 243^{27}=\left(3^5\right)^{27}=3^{135}\)
Vậy \(27^{45}=243^{27}\)