so sánh (1/9)20 và (1/27)13
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
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Đáp án : 9^20 = ( 3^ 2 ) ^ 20 = 3^ 40
27 ^13 = ( 3^3 )^13 = 3 ^39
Vì 3^40 > 3^ 39
Nên suy ra 9^20 > 27^13
![](https://rs.olm.vn/images/avt/0.png?1311)
\(9^{20}=\left(3^2\right)^{20}=3^{40}\)
\(27^{13}=\left(3^3\right)^{13}=3^{39}\)
\(\Rightarrow3^{39}< 3^{40}\)
\(\Leftrightarrow9^{20}>27^{13}\)
Ta có : 920 = ( 32 )20 = 340
2713 = ( 33 )13 = 339
mà 340 > 339
Nên 920 > 2713
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:920=(32)20=340
2713=(33)13=339
Vì 340>339 nên 920>2713
9^20=(3^2)^20=3^40(1)
27^13=(3^3)^13=3^39(2)
Vì 40>39=>3^40>3^39
=>9^20>27^13
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có 9^20= (3^2)^20=3^40
và 27^13=(3^3)^13=3^39
vì 40>39 nên 9^20>27^13
![](https://rs.olm.vn/images/avt/0.png?1311)
920=(32)20=32.20=340
2713=(33)13=33.13=339
Mà 40>39
=>340>339
Vậy 920>2713
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có : 9^20=(3^2)^20=3^40
27^13=(3^3)^13=3^39
vì 3^40>3^39=> 9^20>27^13
ủng hộ nhé
ta có:920=(32)20=340
2713=(33)13=339
vì 40>39=> 340>339 hay 920>2713
Vậy 920>2713
\(\left(\frac{1}{9}\right)^{20}=\left(\left(\frac{1}{3}\right)^2\right)^{20}=\left(\frac{1}{3}\right)^{2.20}=\left(\frac{1}{3}\right)^{40}\)
\(\left(\frac{1}{27}\right)^{13}=\left(\left(\frac{1}{3}\right)^3\right)^{13}=\left(\frac{1}{3}\right)^{3.13}=\left(\frac{1}{3}\right)^{39}\)
Vì 39 < 40 \(\Leftrightarrow\left(\frac{1}{3}\right)^{39}>\left(\frac{1}{3}\right)^{40}\)
\(\left(\frac{1}{27}\right)^{13}>\left(\frac{1}{9}\right)^{20}\)
\(\left(\frac{1}{9}\right)^{20}=\left[\left(\frac{1}{3}\right)^2\right]^{20}=\left(\frac{1}{3}\right)^{40}\)
\(\left(\frac{1}{27}\right)^{13}=\left[\left(\frac{1}{3}\right)^3\right]^{13}=\left(\frac{1}{3}\right)^{39}\)
vì 40 > 39 nên \(\left(\frac{1}{3}\right)^{40}>\left(\frac{1}{3}\right)^{39}\)
hay \(\left(\frac{1}{9}\right)^{20}>\left(\frac{1}{27}\right)^{13}\)