Question

[Minh Tuấn]

so sánh

a)10³⁰và 2¹⁰⁰

b)222⁵⁵⁵và 555²²²

Answer 1

[Alone]

\(10^{30}=\left(10^3\right)^{10}=1000^{10}\)

\(2^{100}=\left(2^{10}\right)^{10}=1024^{10}\)

Vì \(1000^{10}< 1024^{10}\Rightarrow10^{30}< 2^{100}\)

Answer 2

[Phạm Phương Anh]

a, Ta có:

10³⁰ = (10³)¹⁰ = 1000¹⁰

2¹⁰⁰ = (2¹⁰)¹⁰ = 1024¹⁰

Vì 1000 < 1024

=> 1000¹⁰ < 1024¹⁰

hay 10³⁰ < 2¹⁰⁰

b, Ta có:

222⁵⁵⁵ = (222⁵)¹¹¹ = (111⁵.2⁵)¹¹¹

= (111⁵ . 32)¹¹¹

Lại có:

555²²² = (555²)¹¹¹ = (111² . 5²)¹¹¹

= (111² . 25)¹¹¹

Ta có:

111² < 111⁵

=> 111².25 < 111⁵ . 32

=>(111² . 25)¹¹¹ < (111² . 25)¹¹¹

hay 555²²² < 222⁵⁵⁵