Question

Answer 1

a) Ta có:

\(5^{333}=\left(5^3\right)^{111}=125^{111}\)

\(3^{555}=\left(3^5\right)^{111}=243^{111}\)

Vì \(243^{111}>125^{111}\)

⇒\(5^{333}< 3^{555}\)

Answer 2

b) Ta có:

\(2^{400}=\left(2^2\right)^{200}=4^{200}\)

⇒\(2^{400}=4^{200}\)

c) Ta có:

\(5^{300}=\left(5^2\right)^{150}=25^{150}\)

\(3^{453}>3^{450}=\left(3^3\right)^{150}=27^{150}\) 

Vì 25 < 27 nên 5³⁰⁰ < 5⁴⁵³

Answer 3

a) \(5^{333}=\left(5^3\right)^{111}=125^{111}< 3^{555}=\left(3^5\right)^{111}=243^{111}\)

b) \(4^{200}=\left(2^2\right)^{200}=2^{400}\) 

Vì 2⁴⁰⁰ = 2⁴⁰⁰ ⇒ 2⁴⁰⁰ = 4²⁰⁰ 

c) \(5^{300}=\left(5^2\right)^{150}=25^{150}< 3^{453}=\left(3^3\right)^{151}=27^{151}\)