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1: 243^5=(3^5)^5=3^25
3*27^8=3*(3^3)^8=3^25
=>243^5=3*27^8
6: 125^5=(5^3)^5=5^15
25^7=(5^2)^7=5^14
=>125^5>25^7(15>14)
5: 78^12-78^11=78^11(78-1)=78^11*77
78^11-78^10=78^10*77
mà 11>10
nên 78^12-78^11>78^11-78^10
![](https://rs.olm.vn/images/avt/0.png?1311)
a, Ta có: 339 < 340 = (32)20 = 920
1121 > 1120
Vì 9 < 11 => 920 < 1120 => 339 < 1121
b, Ta có: 1245 - 1244 = 1244(12 - 1) = 1244.11
1244 - 1243 = 1243(12 - 1) = 1243.11
Vì 1244 > 1243 => 1244.11 > 1243.11 => 1245 - 1244 > 1244 - 1243
c, Đặt A = 1+2+22+....+29
2A = 2+22+23+...+210
2A-A=210-1
A=210-1
Ta có: 5.28 = 28.4 > 28.4 - 1 = 210 - 1
Vậy A < 5.28
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a) \(33^4=\left(3.11\right)^4=3^4.11^4\\ 44^3=\left(4.11\right)^3=4^3.11^3\)
Ta thấy 34>43 và 114>113 nên 334>443
c) \(54^4=\left(3.18\right)^4=3^4.18^4=3^4.\left(2.9\right)^4=3^4.9^4.2^4=27^4.2^4\\ 21^{12}=\left(3.7\right)^{12}=3^{12}.7^{12}=\left(3^3\right)^4.7^{12}=27^4.7^{12}\)
Ta so sánh 24 với 712
\(7^{12}=\left(7^3\right)^4\)
Nhìn vào ta thấy 2<73 => 24<712=> 544<2112
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1: 243^5=(3^5)^5=3^25
3*27^8=3*3^24=3^25=243^5
3: 3^300=27^100
2^200=4^100
mà 27>4
nên 3^300>2^200
4: 15^2=3^2*5^2
81^3*125^3=3^12*5^9
=>15^2<81^3*125^3
6: 125^5=5^15
25^7=5^14
mà 15>14
nên 125^5>25^7
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\(\dfrac{6}{21}-\dfrac{-12}{44}+\dfrac{10}{12}-\dfrac{-1}{4}-\dfrac{18}{33}\)
\(=\dfrac{6}{21}+\dfrac{12}{44}+\dfrac{10}{12}+\dfrac{1}{4}-\dfrac{18}{33}\)
\(=\dfrac{1013}{924}\)
\(\dfrac{6}{21}-\dfrac{-12}{44}+\dfrac{10}{44}-\dfrac{1}{-4}-\dfrac{18}{33}\)
\(=\dfrac{2}{7}+\dfrac{3}{11}+\dfrac{5}{7}+\dfrac{1}{4}-\dfrac{9}{11}\)
\(=\left(\dfrac{2}{7}+\dfrac{5}{7}\right)+\left(\dfrac{3}{11}-\dfrac{9}{11}\right)+\dfrac{1}{4}\)
\(=1+-\dfrac{6}{11}+\dfrac{1}{4}\)
\(=\dfrac{5}{11}+\dfrac{1}{4}\)
\(=\dfrac{31}{44}\)
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`6/21-(-12/44)+10/14-(1/(-4))-18/33`
`=2/7+12/44+5/7-((-1)/4)-6/11`
`=2/7+3/11+5/7+1/4-6/11`
`=(3/11-6/11)+(2/7+5/7)+1/4`
`=-3/11+7/7+1/4`
`=43/44`
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