1) \(99^{20}=\left(99^2\right)^{10}=9801^{10}< 9999^{10}\)

2) \(3^{21}=3^{20}\cdot3=9^{10}\cdot3\)

\(2^{31}=2^{30}\cdot2=8^{10}\cdot2\)

mà \(9^{10}\cdot3>8^{10}\cdot2\)=> tự viết tiếp

3) đợi chút

4³⁰ = (4³)¹⁰ = 64¹⁰ > 48¹⁰ = ( 2 . 24 )¹⁰ = ( 2¹⁰ ) . ( 24¹⁰ ) > 3 . 24¹⁰
 => 2³⁰ + 3³⁰ + 4³⁰ > 3 . 24¹⁰

.

*99^20=(90^2)^10=8100^10<9999^10

vậy 99^20<9999^10

*3^21=(3^2)10.3=9^10.3

2^31=(2^3)10.2=8^10.2

9^10.3>8^10.2

Vậy 3^21>2^31

a)\(3^{21}< 2^{31}\)

b)\(2^{30}+3^{30}+4^{30}>3.24^{10}\)

Bạn Châu Phạm Bảo ơi! Bạn hãy giải thích hay nêu 

là sao bạn?

a) Ta có: \(99^{20}=\left(99^2\right)^{10}=9801^{10}< 9999^{10}\Rightarrow99^{20}< 9999^{10}\)

b) Ta có: \(2^{31}=\left(2\frac{31}{21}\right)^{21}=2,7822^{21}< 3^{21}\Rightarrow2^{31}< 3^{21}\)

c) Ta có: \(3^{30}=\left(3^3\right)^{10}=27^{10}\)

\(2^{30}=\left(2^3\right)^{10}=8^{10}\)

\(4^{30}=\left(4^3\right)^{10}=64^{10}\)

Lại có: \(3.24^{10}=2.24^{10}+24^{10}\Rightarrow24^{10}< 27^{10}\left(1\right)\)

\(2.24^{10}< 48^{10}< 64^{10}\left(2\right)\)

Từ 1,2 => \(24^{10}+2.24^{10}< 27^{10}+64^{10}\Rightarrow3.24^{10}< 8^{10}+27^{10}+64^{10}\)

\(\Rightarrow3.24^{10}< 3^{30}+2^{30}+4^{30}\)

4^30=2^30*2^30

=2^30*4^15

3*24^10=3*3^10*8^10=3^11*2^30

mà 4^30>3^11

nên 2^30+3^30+4^30>3*24^10

Ta có: 4^30=2^30.2^30=2^30.4^15

3.24^10=3.(3.2^3)^10=2^30.3^11

Ta thấy: 3^11<3^15<4^15 => 4^15>3^11

Vì 4^15>3^11 nên 2^30.4^15>2^30.3^11

=>2^30+3^30+4^30>3.24^10

a) \(2^{30}+3^{30}+4^{30}=4^{15}+27^{10}+64^{10}>4^{15}+24^{10}+2.24^{10}>3.24^{10}\)

b) \(3^{21}=3.9^{10}>3.8^{10}>2.8^{10}=2^{31}\)

bạn trịnh tuấn việt làm đúng rồi đấy

a)Ta có: 
+) 3.24^10 = 3.2^30.3^10 = 2^30.3^11 < 2^30.3^12 = 2^30.9^6.
+) 2^30 + 3^30 + 4^30 = (2^30 + 4^30) + 3^30 > (2^30 + 4^30) 
= 2^30.(1 + 2^30) > 2^30.2^30 = 2^30.32^6

=> (2^30 + 3^30 + 4^30) > 3.24^10

b) 3^21 = (3^7)^3 = 2187^3 
2^31 < 2^33 = (2^11)^3 = 2048^3 
==> 3^21 > 2^33 > 2^31.

\(3\times24^{10}\)

\(=3\times\left(2^3\times3\right)^{10}\)

\(=3\times3^{10}\times\left(2^3\right)^{10}\)

\(=3^{11}\times2^{30}\)

\(=3^{11}\times\left(2^2\right)^{15}\)

\(=3^{11}\times4^{15}\)

Vì \(3^{11}\)<\(4^{15}\left(3;4;11;15\inℕ\right)\)

Nên \(3^{11}\times4^{15}\)< \(4^{15}\times4^{15}=4^{30}\)

Do đó : \(3\times24^{10}\)< \(4^{30}\)

Vậy \(2^{30}+3^{30}+4^{30}\)> \(3\times24^{10}\)

4^30=2^30*2^30

=2^30*4^15

3*24^10=3*3^10*8^10=3^11*2^30

mà 4^30>3^11

nên 2^30+3^30+4^30>3*24^10

4^30=2^30*2^30

=2^30*4^15

3*24^10=3*3^10*8^10=3^11*2^30

mà 4^30>3^11

nên 2^30+3^30+4^30>3*24^10