Question

So sánh 5^40 và 620^10

               7^300 và 5^450

                333^400 và 444^333

Answer 1

5⁴⁰và 620¹⁰

Ta có: 50⁴⁰=(5⁴)¹⁰=625¹⁰

Vì 625>620

=> 625¹⁰<620¹⁰

Vậy 5⁴⁰<620¹⁰

Answer 2

a) \(5^{40}=\left(5^4\right)^{10}=625^{10}\)

Vì \(625^{10}>620^{10}\Rightarrow5^{40}>620^{10}\)

b) \(7^{300}=\left(7^2\right)^{150}=49^{150}\)

\(5^{450}=\left(5^3\right)^{150}=125^{150}\)

Vì \(49^{150}< 125^{150}\Rightarrow7^{300}< 5^{450}\)

c) \(333^{444}=\left(111.3\right)^{444}=111^{444}.3^{444}=111^{444}.\left(3^4\right)^{111}=111^{444}.81^{111}\)

\(444^{333}=\left(111.4\right)^{333}=111^{333}.4^{333}=111^{333}.\left(4^3\right)^{111}=111^{333}.64^{111}\)

Vì \(111^{444}.81^{111}>111^{333}.64^{111}\Rightarrow333^{444}>444^{333}\)

Answer 3

5⁴⁰ = ( 5⁴ )¹⁰ = 625¹⁰

=>625¹⁰ = 625¹⁰

=>5⁴⁰ = 625¹⁰

Answer 4

7³⁰⁰ = ( 7² )¹⁵⁰ = 49¹⁵⁰

5⁴⁵⁰ = ( 5³ )¹⁵⁰ = 125¹⁵⁰

=> 49¹⁵⁰ < 125¹⁵⁰

=> 7³⁰⁰ < 5⁴⁰⁰