Question

So sánh:

     a) 3⁵⁰⁰ và  7³⁰⁰

     b) 9¹² và 27⁷

Answer 1

a) 3⁵⁰⁰ = (3⁵)¹⁰⁰ = 243¹⁰⁰

7³⁰⁰ = ( 7³ )¹⁰⁰ = 343¹⁰⁰

Vì 343 > 243 => 7³⁰⁰ > 3⁵⁰⁰

b) 9¹² = ( 3² )¹² = 3²⁴

27^7 = ( 3³ )⁷ = 3²¹

Vì 3²⁴ > 3²¹ => 9¹² > 27⁷

Answer 2

a) Ta có:

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

\(7^{300}=7^{3.100}=\left(7^3\right)^{100}=343^{100}\)

Vì \(243^{100}< 343^{100}\Rightarrow3^{500}< 7^{300}\)

b) Ta có:

\(9^{12}=\left(3^2\right)^{12}=3^{24}\)

\(27^7=\left(3^3\right)^7=3^{21}\)

Vì \(3^{24}>3^{21}\Rightarrow9^{12}>27^7\)