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Ta có:
\(5^{225}=5^{15.17}=\left(5^{15}\right)^{17}\)=3051757812517
2^572=2^16.17=(2^16)^17=65536^17
=>5^255 > 2^572
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Mk giải hộ
5^255 = 5^(3*75) = (5^3)^75 = 125^75
2^572 > 2^525
2^525 = 2^(7*75) = (2^7)^75 = 128^75
=> 2^572 > 128^75
128^75 > 125^75
=> 2^572 > 2^525 > 125^75
Đáp số:
2^572 > 5^255
Ta có : 54 > 29 ( vì 625 > 512 )
=> ( 54 )64 > ( 29 )64
=> 5256 > 2576
=> 5256 : 5 > 2576 : 5 > 2576 : 8
=> 5255 > 2576 : 23
=> 5255 > 2573 > 2572
=> 5255 > 2572
Vậy 5255 > 2572
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(5^4=625\)
\(2^9=512\)
\(\Rightarrow5^4>2^9\)
\(\Rightarrow\left(5^4\right)^{64}>\left(2^9\right)^{64}\)
\(\Rightarrow5^{255}>\dfrac{2^{576}}{5}>\dfrac{2^{576}}{2^3}=2^{573}>2^{572}\)
\(\Rightarrow\)\(5^{255}>2^{572}\)
Vậy: \(5^{255}>2^{572}\)
Chúc bạn học tốt!!!!!
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
5^255 = 5^3.75 = 125^75
2^579 > 2^525 = 2^7.75= 128^75
Như vậy: 2^579 > 128^75 > 125^75 = 5^255
Vậy: 2^579 > 2^255
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
5^4 = 625 ; 2^9 = 512
=> 5^4 > 2^9
=> (5^4)^64 > (2^9)^64
=> 5^255 > 2^576 / 5 > 2^576 / 2^3 = 2^573 > 2^572
Vậy 5^255 > 2^572