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

ta có

2 mũ 3 = 8

3 mũ 2=9

vì 8<9 nên 2 mũ 3 <3 mũ 2

b/ Ta có: 2⁹¹>2⁹⁰=(2⁵)¹⁸=32¹⁸>25¹⁸=(5²)¹⁸=5³⁶>5³⁵    =>     2⁹¹>5³⁵

c/ Ta có: 2²²⁵=(2³)⁷⁵=8⁷⁵

              3¹⁵⁰=(3²)⁷⁵=9⁷⁵

Vì 8⁷⁵<9⁷⁵ nên 2²²⁵<3¹⁵⁰

a)Ta có:  2^27=(2^3)^9=8^9

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

Vì  8^9 <9^9

2^27<3^18

d)Ta có :27^7=(3^3)^7=3^21

9^12=(3^2)^12=3^24

Vì 3^21<3^24

27^7<9^12

a, 2³⁰⁰ = (2³)¹⁰⁰ = 8¹⁰⁰

3²⁰⁰ = (3²)¹⁰⁰ = 9¹⁰⁰

Vì 8¹⁰⁰ < 9¹⁰⁰

=> 2³⁰⁰ < 3²⁰⁰

b, 2²⁰ = (2⁵)⁴ = 32⁴

3¹² = (3³)⁴ = 27⁴

Vì 32⁴ > 27⁴

=> 2²⁰ > 3¹²

c, 2²²⁵ = (2³)⁷⁵ = 8⁷⁵

3¹⁵⁰ = (3²)⁷⁵ = 9⁷⁵

Vì 8⁷⁵ < 9⁷⁵

=> 2²²⁵ < 3¹⁵⁰

d, 21¹⁵ = (3.7)¹⁵ = 3¹⁵.7¹⁵

27⁵.49⁸ = (3³)⁵.(7²)⁸ = 3¹⁵.7¹⁶

Vì 3¹⁵.7¹⁵ < 3¹⁵.7¹⁶

=> 21¹⁵ < 27⁵.49⁸

59¹⁸​>23⁵⁴

^​​​​ai tochs mk mk sẽ tích lại

Ta có: 23⁵⁴ = 23^3x18 = (23³)¹⁸ = 12167¹⁸

 Vì 59 < 12167 => 59¹⁸ < 12167¹⁸ hay 59¹⁸ < 23⁵⁴.

Chuẩn rồi đó _{Tích nha bạn}

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 \(\frac{27}{45}>\frac{18}{36}\)