\(10^{30}=\left(10^3\right)^{10}=1000^{10}\)
\(2^{100}=\left(2^{10}\right)^{10}=1024^{10}\)
Vì \(1000^{10}< 1024^{10}\Rightarrow10^{30}< 2^{100}\)
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
b, ta có 222555=25.1115=32.1115
555222=52. 1112=25.1112
Do 32> 25 , 1115> 1112
=> 32.1115 >25.1112
Hay 222555 > 555222
