\(2^{91}=\left(2^{13}\right)^7=73728^7\)

\(5^{35}=\left(5^5\right)^7=3125^7\) nhỏ hơn \(73728^7\)

\(\Rightarrow2^{91}\) lớn hơn \(5^{35}\)

\(b,3^{400}=\left(3^4\right)^{100}=81^{100}\\ 4^{300}=\left(4^3\right)^{100}=64^{100}\\ Vì:81^{100}>64^{100}\left(Do:81>64\right)\\ \Rightarrow3^{400}>4^{300}\)

\(d,10^{20}=\left(10^2\right)^{10}=100^{10}\\ Vì:100^{10}>20^{10}\left(Do:100>20\right)\\ \Rightarrow10^{20}>20^{10}\)

a, Ta có:

\(2^{225}=2^{3.75}=\left(2^3\right)^{75}=8^{75}\)

\(3^{150}=3^{2.75}=\left(3^2\right)^{75}=9^{75}\)

Vì \(8^{75}< 9^{75}\)nên \(2^{225}< 3^{150}\)

b, Ta có:

\(2^{91}=2^{13.7}=\left(2^{13}\right)^7=8192^7\)

\(5^{35}=5^{5.7}=\left(5^5\right)^7=3125^7\)

Vì \(8192^7>3125^7\)nên \(2^{91}>5^{35}\)

2^225>3^150

2^91<5^35

99^20<9999^10

a, 2²²⁵ và 3¹⁵⁰
2²²⁵ = ( 2³ )⁷⁵ = 8⁷⁵
3¹⁵⁰ = ( 3² )⁷⁵ = 9⁷⁵
Do 8⁷⁵ < 9⁷⁵ nên 2²²⁵ < 3¹⁵⁰ 
b,c tương tự
 

Viết rối qá chả thấy j.

\(99^2vs9999^{10}\)

\(9999^{10}=\left(101\cdot99\right)^{10}=101^{10}\cdot99^{10}\)

Vì \(99^{10}>99^2=>99^2< 9999^{10}\)

a) Ta có: 2^91 = (2^13)^7 = 8192^7

5^35 = (5^5)^7 = 3125^7

Vì 8192 > 3125 nên 8192^7 > 3125^7

Vậy 2^91 > 5^35

b) Ta có: 9999^10 = 99^10 . 101^10

Vì 99^2 < 99^10 nên 99^2 < 99^10 . 101^10

Vậy 99^2 < 9999^10

c) Ta có: 2^300 = (2^6)^50 = 64^50

3^200 = (3^4)^50 = 81^50

Vì 49 < 64 < 81 nên 49^50 < 64^50 < 81^50

Vậy 49^50 < 2^300 < 3^200

d) 9^3/25^3 = (9/25)^3

3^6/2^12 = (3^2)^3/(2^4)^3 = 9^3/16^3 = (9/16)^3

Vì 9/25 < 9/16 nên (9/25)^3 < (9/16)^3

Vậy 9^3/25^3 < 3^6/2^12.

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 2²²⁵ = (2³)⁷⁵ = 8⁷⁵

3¹⁵⁰ = (3²)⁷⁵ = 9⁷⁵

Vậy 2²²⁵ < 3¹⁵⁰

Ta có:

2⁹¹ = (2¹³)⁷ = 8192⁷

5³⁵ = (2⁵)⁷ = 3125⁷ 

Vì 8192⁷ > 3125⁷

=> 2⁹¹ > 5³⁵

Ta có:

99²⁰ = 99¹⁰.99¹⁰ < 99¹⁰.100¹⁰ < 99¹⁰.101¹⁰ = 9999¹⁰

=> 99²⁰ < 9999¹⁰

2²⁵⁵ > 3¹⁵⁰

2⁹¹ < 5³⁵

99²⁰ < 9999¹⁰

bạn dùng máy tính casio ccũng được

a) Ta có: \(2^{225}=2^{3.75}=\left(2^3\right)^{75}=8^{75}\)

                \(3^{150}=3^{2.75}=\left(3^2\right)^{75}=9^{75}\)

\(\Rightarrow8^{75}< 9^{75}\)\(\Rightarrow2^{225}< 3^{150}\)

b) Ta có : \(2^{91}=2^{7.13}=\left(2^{13}\right)^7=8192^7\)

                \(5^{35}=5^{5.7}=\left(5^5\right)^7=3125^7\)

\(\Rightarrow8192^7>3125^7\)\(\Rightarrow2^{91}>3^{35}\)

c) Ta có: \(99^{20}=99^{2.10}=\left(99^2\right)^{10}=\left(99.99\right)^{10}\)

               \(9999^{10}=\left(99.101\right)^{10}\)

Vì 99<101 \(\Rightarrow\left(99.99\right)^{10}< \left(99.101\right)^{10}\)\(\Rightarrow99^{20}< 9999^{10}\)

a, 2^24 > 3^16

b, 5^300>3 ^500

c,99^20 > 9999^10

d, 2^30 +3^44 +4^30 < 3x24^10