Ta có :

         = (2³)¹⁰ + (3³)¹⁰ + (4³)¹⁰

         = 8¹⁰ + 27¹⁰ + 64¹⁰

         = ( 3²)¹⁰ + (6²)¹⁰ + (8²)¹⁰

         ⁼ 9¹⁰ + 36¹⁰ + 64¹⁰

Ta thấy: 8¹⁰ + 27¹⁰ + 64¹⁰ < 9¹⁰ + 36¹⁰ + 64¹⁰

\(\Rightarrow\) 2³⁰ + 3³⁰ + 4³⁰ < 3²⁰ + 6²⁰ + 8²⁰

     <

a/ 40^20=40^2.10=1600^10

3^30=3^3.10=27^10

vì 1600^10>27^10 nên 40^20>3^30

a) 40^20=(4^2)^10=16^10

30^30=(3^3)^10=27610

Vì 16<27=>16^10<27^10 hay 4^20<3^30

b) mk chịu

c) Đặt A= 1/3+1/3^2+1/3^3+...+1/3^99

=>3A=3( 1/3+1/3^2+1/3^3+...+1/3^99)

=>3A=1+1/3+1/3^2+...+1/3^98

=>3A-A=(1+1/3+1/3^2+...+1/3^98)-(1/3+1/3^2+1/3^3+...+1/3^99)

=>2A=1-1/3^99

=>A=(1-1/3^99)/2

=>A=1/2 - (1/3^99)/2 < 1/2=>a<1/2

               Bài làm :

\(1\text{)}\hept{\begin{cases}5^{30}=\left(5^3\right)^{10}=125^{10}\\3^{50}=\left(3^5\right)^{10}=243^{10}\end{cases}}\Rightarrow5^{30}< 3^{50}\)

\(2\text{)}\hept{\begin{cases}27^3=\left(3^3\right)^3=3^9\\9^5=\left(3^2\right)^5=3^{10}\end{cases}}\Rightarrow27^3< 9^5\)

\(3\text{)}14^{40}>14^{20}\)

\(4\text{)}\hept{\begin{cases}2< 12\\15< 16\end{cases}}\Rightarrow2^{15}< 12^{16}\)

2²⁰ = (2⁵)⁴ = 32⁴

3¹² = (3³)⁴ = 27⁴

Do 32 > 27 nên 32⁴ > 27⁴

Vậy 2²⁰ > 3¹²

2²⁰ = (2⁵)⁴ = 32⁴

3¹² = (3³)⁴ = 27⁴

Vì 32 > 27 ⇒ 32⁴ > 27⁴ ⇒ 2²⁰ > 3¹²

Cảm ơn m.n nhiều.

a) Ta có : 4²⁰ = (4²)¹⁰ = 16¹⁰

              3³⁰ = (3³)¹⁰ = 27¹⁰

Vì 16¹⁰ < 27¹⁰ nên 4²⁰ < 3³⁰

b) Ta có : 7²¹ = (7³)⁷ = 343⁷ 

               8¹⁴ = (8²)⁷ = 64⁷

Vì 343⁷ > 64⁷ nên 7²¹ > 8¹⁴

5 phần 1o

a: \(2^{225}=8^{75}\)

\(3^{150}=9^{75}\)

mà 8<9

nên \(2^{225}< 3^{150}\)

b: \(2^{91}=8192^7\)

\(5^{35}=3125^7\)

mà 8192>3125

nên \(2^{91}>5^{35}\)