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\(16^{15}=\left(2^4\right)^{15}=2^{60}\)
\(128^9=\left(2^7\right)^9=2^{63}\)
\(2^{60}< 2^{63}\Rightarrow16^{15}< 128^9\)
\(16^{15}=(2^4)^{15}=2^{60}\)
\(128^9=(2^7)^9=2^{63}\)
Mà 260 < 263 => \(16^{15}< 128^9\)
Vậy : .....
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27/82 và 26/75
Ta có:
27/82 = 2025/6150
26/75 = 2132/6150
Vì 2025/6150<2132/6150 nên 27/82<26/75.
Vậy: 27/82<26/75.
![](https://rs.olm.vn/images/avt/0.png?1311)
`M=(10^25+1)/(10^26+1)`
`=>10M=(10^26+10)/(10^26+1)=1+9/(10^26+1)``
`CMTT:10N=1+9/(10^27+1)`
Vì `1/(10^26+1)>1/(10^27+1)`
`=>9/(10^26+1)>9/(10^27+1)`
`=>1+9/(10^26+1)>1+9/(10^27+1)`
`=>10M>10N=>M>N`
![](https://rs.olm.vn/images/avt/0.png?1311)
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\(A=10^{25}+\frac{1}{10^{26}}+1=1\cdot10^{25}\)
\(B=10^{26}+\frac{1}{10^{27}}+1=1\cdot10^{26}\)
\(1\cdot10^{25}< 1\cdot10^{26}\Rightarrow A< B\)
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ta có \(26^2-24^2=\left(26-24\right).\left(26+24\right)=2.50\)
\(27^2-25^2=\left(27-25\right).\left(27+25\right)=2.52\)
vậy \(27^2-25^2>26^2-24^2\)
So sánh A = 26^2 - 24^2 và B = 27^2 - 25^2
A = 26^2 - 24^2=(26+24)(26-24)=50*2=100
B = 27^2 - 25^2=(27+25)(27-25)=52*2=104
mà 104>100
=>B>A
![](https://rs.olm.vn/images/avt/0.png?1311)
c) \(\dfrac{27}{26}\)và\(\dfrac{38}{37}\)
Ta có: \(\dfrac{27}{26}=1+\dfrac{1}{26}\); \(\dfrac{38}{37}=1+\dfrac{1}{37}\)
Vì \(\dfrac{1}{26}>\dfrac{1}{37}\) nên \(\dfrac{27}{26}>\dfrac{38}{37}\)
c: \(\dfrac{27}{26}-1=\dfrac{1}{26}\)
\(\dfrac{38}{37}-1=\dfrac{1}{37}\)
mà \(\dfrac{1}{26}>\dfrac{1}{37}\)
nên \(\dfrac{27}{26}>\dfrac{38}{37}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
12815 & 2726
12815 < 12915
12915 = 315. 4315 < 315 . 315. 315. 315. 315 = 315.360
2726 = 315. 311 . 315 . 311 . 315 . 311 = 315. 363
⇒ 12915 < 2726
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