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\(10^{30}=\left(10^3\right)^{10}=1000^{10}\)
\(2^{100}=\left(2^{10}\right)^{10}=1024^{10}\)
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
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(7^{n+4}-7^n\)
\(=7^n\left(7^4-1\right)\)
\(=7^n.2400⋮100\)
b) \(20^5\equiv1\left(mod11\right)\)
\(\Rightarrow20^{15}\equiv1\left(mod11\right)\)
\(\Rightarrow20^5-1\equiv0\left(mod11\right)\)
\(\Rightarrow20^5-1⋮11\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left\{{}\begin{matrix}ac=b^2\Rightarrow\frac{a}{b}=\frac{b}{c}\\ab=c^2\Rightarrow\frac{b}{c}=\frac{c}{a}\end{matrix}\right.\) \(\Rightarrow\frac{a}{b}=\frac{b}{c}=\frac{c}{a}=\frac{a+b+c}{b+c+a}=1\Rightarrow a=b=c\)
\(\Rightarrow P=1+1+1=3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có 222^555=(2^5.111^5)^111
555^222=(5^2.111^2)^111
Mà 2^5.111^5=32.111^5>25.111^2=5^2.111^2
=> 222^555>555^222
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\text{Ta có : A}=222^{555}=(222^5)^{111}\)
\(\text{B}=555^{222}=(555^2)^{111}\)
\(\text{Vì }222^{555}-555^{222}>0\Rightarrow A>B\)
Chúc bạn học tốt :>
\(\text{Có j thắc mắc thì cứ hỏi mk}\)
ta có:
A=222555=(2225)111
B=555222=(5552)111
=>A>B vì 2225>5552
vậy A>B
![](https://rs.olm.vn/images/avt/0.png?1311)
676 + 555 - 100 = 676 + 555 = 1231 = 1231 - 100 = 1131
34.32.35 = 3(4 + 2 + 5)= 311