10³và 2¹⁰⁰

Ta có:10³⁰=(10³)¹⁰=1000¹⁰

          2¹⁰⁰=(2¹⁰)¹⁰=1024¹⁰

Vì 1000<1024 nên 10³⁰<2¹⁰⁰

5³⁰⁰ và 3⁴⁵³

Ta có:5³⁰⁰=(5²)¹⁵⁰=25¹⁵⁰

            3⁴⁵³=(3³)¹⁵¹=27¹⁵¹=27.27¹⁵⁰

Vì  25 < 27.27 nên 5³⁰⁰<3⁴⁵³

nhớ k ch mình nhé

\(2^{27}=2^{3.9}=8^9\)

\(3^{18}=3^{2.9}=9^9\)

Vì \(9^9>8^9\Rightarrow3^{18}>2^{27}\)

MK chỉ làm đc câu a) thui nha :

2^27 = 2^ 3.9 = 8^9

3^18 = 3^2.9=9^9

Vì 9^9 > 8^9 => 2^27 < 2 ^18 

a) ta có: 2⁹⁰ = (2⁵)¹⁸ = 32¹⁸

5³⁶ = (5²)¹⁸ = 25¹⁸

=> ...

b) 2²⁷ = (2³)⁹ = 8⁹

3¹⁸ = (3²)⁹ = 9⁹

=>...

a)

2^90 = (2^10)^9 = 1024^9

5^36 = (5^4)^9 = 625^9

Mà 1024^9 > 625^9 => 2^90 > 5^36

Vậy 2^90 > 5^36

b)

2^27 = (2^3)^9 = 8^9

3^18 = (3^2)^9 = 9^9

Mà 8^9 > 9^9 => 2^27 > 3^18

Vậy 2^27 > 3^18

k mik nha mn !    ^ - ^

Ta có: \(99^{20}=\left(99^2\right)^{10}=9801^{10}\)

Vì \(9801< 9999\)nên \(9801^{10}=9999^{10}\)

Vậy \(99^{20}< 9999^{10}\)

a, 2^27 = 2^3.9 = 8^9 

3^18 = 3^2.9 = 9^9 

vì 8<9 => 8^9 < 9^9 => 2^27 < 3^18

a) 3²⁰⁰=(3²)¹⁰⁰=9¹⁰⁰ ; 2³⁰⁰=(2³)¹⁰⁰=8¹⁰⁰

=> 9¹⁰⁰>8¹⁰⁰ hay 3²⁰⁰>2³⁰⁰

b) 71⁵⁰=(71²)²⁵=5041²⁵ ; 37⁷⁵=(37³)²⁵=50653²⁵

=> 5041²⁵<50653²⁵ hay 71⁵⁰<37⁷⁵

c)rút gọn

2016014/2017015=2014/2015

2016016014/2017017015=2014/2015

=> 2014/2015 = 2014/2015

mình làm câu b thôi nhé câu a từ từ mình làm

b/ 2^27 và 3^18

Ta có 2^27= ( 2^3 )^9=8^9

3^18= (3^2)^9=9^9

vì 8^9<9^9

suy ra 2^27<3^18

\(2^{90}=2^{5.18}=\left(2^5\right)^{18}=32^{18}\)

\(5^{36}=5^{2.18}=\left(5^2\right)^{18}=25^{18}\)

Vì \(32^{18}>25^{18}\Rightarrow2^{90}>5^{36}\)

b, 

\(2^{27}=2^{3.9}=\left(2^3\right)^9=8^9\)

\(3^{18}=3^{2.9}=\left(3^2\right)^9=9^9\)

Vì \(8^9< 9^9\Rightarrow2^{27}< 3^{18}\)

Bài 1:

a: Cách 1: \(\frac37=\frac{3\cdot9}{7\cdot9}=\frac{27}{63};\frac59=\frac{5\cdot7}{9\cdot7}=\frac{35}{63}\)

mà 27<35

nên \(\frac37<\frac59\)

Cách 2: Ta có: \(\frac37=\frac{3\cdot5}{7\cdot5}=\frac{15}{35}\)

\(\frac59=\frac{5\cdot3}{9\cdot3}=\frac{15}{27}\)

mà \(\frac{15}{35}<\frac{15}{27}\left(35>27\right)\)

nên \(\frac37<\frac59\)

b: Cách 1: \(\frac{6}{12}=\frac{6\cdot3}{12\cdot3}=\frac{18}{36};\frac49=\frac{4\cdot4}{9\cdot4}=\frac{16}{36}\)

mà 18>16

nên \(\frac{6}{12}>\frac49\)

Cách 2: \(\frac{6}{12}=\frac{6\cdot2}{12\cdot2}=\frac{12}{24};\frac49=\frac{4\cdot3}{9\cdot3}=\frac{12}{27}\)

mà \(\frac{12}{24}>\frac{12}{27}\left(24<27\right)\)

nên \(\frac{6}{12}>\frac49\)

c: Cách 1: \(\frac{15}{25}=\frac{15\cdot18}{25\cdot18}=\frac{270}{450};\frac{54}{90}=\frac{54\cdot5}{90\cdot5}=\frac{270}{450}\)

Do đó: \(\frac{15}{25}=\frac{54}{90}\)

Cách 2: \(\frac{15}{25}=\frac{15:5}{25:5}=\frac35;\frac{54}{90}=\frac{54:18}{90:18}=\frac35\)

do đó: \(\frac{15}{25}=\frac{54}{90}\)

d: Cách 1: \(\frac{25}{30}=\frac{25\cdot3}{30\cdot3}=\frac{75}{90};\frac{75}{28}=\frac{75\cdot1}{28\cdot1}=\frac{75}{28}\)

mà \(\frac{75}{90}<\frac{75}{28}\left(90>28\right)\)

nên \(\frac{25}{30}<\frac{75}{28}\)

Cách 2: \(\frac{25}{30}=\frac{25\cdot14}{30\cdot14}=\frac{350}{420}\)

\(\frac{75}{28}=\frac{75\cdot15}{28\cdot15}=\frac{1125}{420}\)

mà 350<1125

nên \(\frac{25}{30}<\frac{75}{28}\)

e: cách 1: \(\frac{27}{45}=\frac{27\cdot4}{45\cdot4}=\frac{108}{180};\frac{18}{36}=\frac{18\cdot5}{36\cdot5}=\frac{90}{180}\)

mà 108>90

nên \(\frac{27}{45}>\frac{18}{36}\)

Cách 2: \(\frac{27}{45}=\frac{27\cdot2}{45\cdot2}=\frac{54}{90}\)

\(\frac{18}{36}=\frac{18\cdot3}{36\cdot3}=\frac{54}{108}\)

mà \(\frac{54}{90}>\frac{54}{108}\left(90<108\right)\)

nên \(\frac{27}{45}>\frac{18}{36}\)