\(50^2< 50^3\)

Quá dễ bạn ơi

#EZ

50 = 50 

2 <3 

Vậy 50\(^2\)<  50 \(^3\)

Dễ mà :(((

50² và50^{3 ( 2<3)}

\(\sqrt{29}+\sqrt{3}+\sqrt{2003}>\sqrt{25}+\sqrt{1}+\sqrt{1936}=5+1+44=50\)

\(\text{Vậy }\sqrt{29}+\sqrt{3}+\sqrt{2003}>50\)

\(\sqrt{29}+\sqrt{3}+\sqrt{2013}>\sqrt{25}+\sqrt{1}+\sqrt{1936}=5+1+44=50\)

Ta có:

  \(3^{100}=\left(3^2\right)^{50}=9^{50}\) 

Mà \(8^{50}< 9^{50}\)

Vậy \(8^{50}< 3^{100}\)

8⁵⁰=(8²)²⁵=64²⁵

3¹⁰⁰=(3⁴)²⁵=81²⁵

Mà 64²⁵<81²⁵

Vậy 8⁵⁰<3¹⁰⁰

Ta có :

\(7^{100}=7^{2\cdot50}=\left(7^2\right)^{50}=49^{50}\)

Vì 49^50 < 50^50

Nên 7^100 < 50^50

\(\left(-2\right)^{100}=2^{100}=\left(2^2\right)^{50}=4^{50}=\left(-4\right)^{50}\)

Ủa bn Ý lớp mik hả , hs giỏi ah

\(a=2^{100}=\left(2^4\right)^{25}=16^{25}\)

\(b=3^{75}=\left(3^3\right)^{25}=27^{25}\)

\(c=5^{50}=\left(5^2\right)^{25}=25^{25}\)

Vì \(16^{25}< 25^{25}< 27^{25}\)

\(\Rightarrow a< c< b\)

\(a=2^{100},b=3^{75},c=5^{50}\\ \Rightarrow a=30^{85},b=30^{65},c=30^{44}\\ \Rightarrow a>b>c\)

Ta có:

\(a=2^{100}=2^{4\cdot25}=\left(2^4\right)^{25}=16^{25}\)

\(b=3^{75}=3^{3\cdot25}=\left(3^3\right)^{25}=27^{25}\)

\(c=5^{50}=5^{2\cdot25}=\left(5^2\right)^{25}=25^{50}\)

Ta thấy: 

\(16< 25< 27\)

\(\Rightarrow16^{25}< 25^{25}< 27^{25}\)

\(\Rightarrow2^{100}< 5^{50}< 3^{75}\)

\(\Rightarrow a< c< b\)

> nhé bạn           

cho 149 là 150

7¹⁵⁰ = 7^3.50 = 343⁵⁰

345⁵⁰ = 345^1.50 = 345⁵⁰

Mà 343⁵⁰ < 345⁵⁰    Nên:

7¹⁴⁹   <345⁵⁰

Cho 199 là 200

3²⁰⁰ = 3^2.100 = 9¹⁰⁰

11¹⁰⁰ = 11^1.100 = 11¹⁰⁰     Mà

9¹⁰⁰  < 11¹⁰⁰      Nên

3¹⁹⁹  <  11¹⁰⁰

7^149 < 7^150 = 343^50 < 345^50 => 7^149 < 345^50

3^199 < 3^200 = 9^100 < 11^100 => 3^199 <11^100