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a) ta có: 1512 = 312.512
813.1255 = (34)3.(53)5 = 312.515 > 312.512
=> ...
b) ta có: 3452 = 345.345 = 342.345 + 345.3
342 .348 = 342.345 + 342.3 < 342.345 + 345.3
=> ...
c) ta có: 320 = (32 )10 = 910
230 = (23)10 = 810
=> ....
d) ta có: 4500 = (45)100 = 1024100
5400 = (54)100 = 625100
=> ....
e) ta có: 1255 > 1085 =275.45 = 275.1024
277 = 275.272 = 275.729
=> ...
a)
ta có :
53.10 = ( 53)10 = 12510
12510 > 1259
=> 530 > 1259
các phần còn lại bạn làm tượng tự nha
a) \(125^9=\left(5^3\right)^9=5^{27}< 5^{30}\)
b) \(16^{25}=\left(2^4\right)^{25}=2^{100}\)
\(8^{50}=\left(2^3\right)^{50}=2^{150}\)
Vì mũ 100 < mũ 150 và 2 cơ số bằng nhau
=>\(16^{25}< 8^{50}\)
c) \(3^{20}=3^{2.10}\)
\(2^{40}=2^{4.10}\)
\(\Rightarrow3^2=9\)
\(2^4=16\)
Vì 9 < 16
=> \(2^{40}>3^{20}\)
a) 12 : { 400 : [500 – (125 + 25 . 7)]}
=12 : { 400 : [500 – (125 + 175)]}
=12 : [ 400 : [500 – 300)]
=12 : (400:200)
=12:2=6
b) 5 . 22 – 18 : 3
=5.4-6
=20-6=14
c) 18 : 3 + 182 + 3.(51 : 17)
=5+182+3.3
=187+9=196
d) 25 . 8 – 12.5 + 170 : 17 – 8
=200-60+10-8
=142
e) 2.52+ 3: 710 – 54: 33
=2.25+3:1-54:27
=50+3-2
=51
f) 189 + 73 + 211 + 127
=(189+211)+(73+127)
=400+200=600
g) 375 : {32 – [ 4 + (5. 32– 42)]} – 14 )
=375 : {32 – [ 4 + (160– 42)]} – 14 )
=375 : [32 – ( 4 + 118) – 14 ]
=375:(32-122-14)
=375:-104
=-375/104
h) (52022 + 52021) : 52021
=(52022:52021)+(52021:52021)
=5+1=6
1. \(5656^{500}>56^{500}>56^{100}\)
2. \(333^4< 444^4< 444^{333}\)
3.\(345^2>345^2-3^2=342\times348\)
4.\(2^{100}=\left(2^{10}\right)^{10}=1024^{10}>1024^9\)
5.\(107^{50}=11449^{25}< 389017^{25}=73^{75}\)
6.\(2^{91}< 5^{35}\)
7. \(19^{20}=361^{10}>225^{10}>225^8=9^8\times5^{16}\)
8. \(54^4< 9261^4=21^{12}\)
a) = - 15.9+5 = -45 + 5 = - 40
b) -31.9 +31. 2,5=31. (-9 + 2,5) = 31 . ( - 6,5) =-201,5
c) 5. (-27) - 36 : 36 = -135 -1=-136
d) = -147 - [68+8.4]:25 =-147 -100: 25 = -147 - 4 = -151
e) -141 +64+(-8)=-77 + ( -8) = -85
g) -20 - 11 - 500:[4.25]+76 =-31- 500: 100 +76 = -31 -5 +76 = - 36 + 76 = 40
1) ( -15 ) . (-3 )2 - 250 : ( -50 )
=( -15 ) . 9 - 250 : ( -50 )
= -135 - ( -5 )
= -130
2) ( -31 ) .32 + 310 : (-2 )2
= (-31). 9+ 310: 4
= 279+ 77, 5
= 365,5
1005 : 1003 = 1002
102 . 101 = 103
500200 . 50010 = 500210
105 . 102 = 107
10030 . 10010 = 10040
200100 : 20010 = 20090
10020 . 10010 = 10030
300100 . 300100 = 300200
1005 : 1003
= 1005 - 3
= 1002
102 . 101
= 102 + 1
= 103
500200 . 50010
= 500200 + 10
= 500210
105 . 102
= 105 + 2
= 107
10030 . 10010
= 10030 + 10
= 10040
200100 : 20010
= 200100 - 10
= 200190
10020 . 10010
= 10020 + 10
= 10030
300100 .300100
= 300100 + 100
= 300200
a, A = \(\dfrac{3^9\times3^{20}\times2^8}{3^{24}\times243\times2^6}\)
A = \(\dfrac{3^{29}\times2^8}{3^{24}\times3^5\times2^6}\)
A = \(\dfrac{3^{39}\times3^{20}\times2^8}{3^{29}\times2^6}\)
A = 22
A = 4
b, \(\dfrac{2^{15}\times5^3\times2^6\times3^4}{8\times2^{18}\times81\times5}\)
B = \(\dfrac{2^{21}\times3^4\times5^3}{2^3\times2^{18}\times3^4\times5}\)
B = \(\dfrac{2^{21}\times3^4\times5^3}{2^{21}\times3^4\times5}\)
B = 52
B = 25
\(15.30+15.73-15.13=15.\left(30+73-13\right)=15.90=1350\)
\(5^2.165-56.5^2=5^2.\left(165-56\right)=5^2.109=2725\)
\(=55:\left\{400:144\right\}=55:2,7=20,3\)