Question

So sánh

a. 4^2222 và 2^4444

b.5^300 và 3^500

Answer 1

4 = 2^2 => 4 ^a =2^2a 

mà 2222*2 =4444 => 2^4444=4^2222

Answer 2

a hai cái bằng nhau

b 3 ^ 500 lớn hơn

Answer 3

a)Ta có :  \(4^{2222}\) \(=4^{2.1111}=\left(4^2\right)^{1111}=16^{1111}\)

\(2^{4444}=2^{4.1111}=\left(2^4\right)^{1111}=16^{1111}\)

Vì \(16^{1111}=16^{1111}\Rightarrow4^{2222}=2^{4444}\)

b) Ta có : \(5^{300}=5^{3.100}=\left(5^3\right)^{100}=125^{100}\)

\(3^{500}=3^{5.100}=\left(3^5\right)^{100}=243^{100}\)

Vì \(125^{100}< 243^{100}\Rightarrow5^{300}< 3^{500}\)

Answer 4

a, 4²²²² = 4^{2 . 1111} = (4²)¹¹¹¹ = 16¹¹¹¹

    2⁴⁴⁴⁴ = 2^{4 . 1111} = (2⁴)¹¹¹¹ = 16¹¹¹¹

Mà 16¹¹¹¹ = 16¹¹¹¹ => 4²²²² = 2⁴⁴⁴⁴

b, 5³⁰⁰ = 5^{3 . 100} = (5³)¹⁰⁰ = 125¹⁰⁰

3⁵⁰⁰ = 3^{5 . 100} = (3⁵)¹⁰⁰ = 243¹⁰⁰

Vì 125¹⁰⁰ < 243¹⁰⁰ nên 5³⁰⁰ < 3⁵⁰⁰ 

Answer 5

Ta có 

a) \(4^{2222}=\left(4^2\right)^{1111}=16^{1111}\)

\(2^{4444}=\left(2^4\right)^{1111}=16^{1111}\)

mà \(16^{1111}=16^{1111}\)nên \(4^{2222}=2^{4444}\)

b) \(5^{300}=\left(5^3\right)^{100}=125^{100}\)

\(3^{500}=\left(3^5\right)^{100}=243^{100}\)

mà \(125^{100}< 243^{100}\)nên\(5^{300}< 3^{500}\)

Answer 6

\(Tacó:4^{2222}với2^{4444}\)

Mà \(4^{2222}=\left(2^2\right)^{2222}=2^{4444}\)

Ta thấy \(2^{4444}=2^{4444}\)

\(\Rightarrow4^{2222}=2^{4444}\)

\(b,5^{300}với3^{500}\)

Ta thấy \(5^{300}=\left(5^3\right)^{100};3^{500}=\left(3^5\right)^{100}\)

\(\Rightarrow5^{300}=125^{100};3^{500}=243^{100}\)

Mà\(243^{^{100}}>125^{^{100}}\)

\(\Rightarrow5^{300}< 3^{500}\)

Answer 7

a, ta co : 4^2222 = 4^(1111 . 2 ) = 4^1111 . 4^2 =4^1111 . 16

    ta co : 2 ^ 4444=2^(1111.4)=2^1111 . 4^2=2^1111.16

Vi 16=16 ; 4^1111 > 2^1111 nen suy ra 4^2222 > 2^4444

tuong tu 3^500 lon hon