(-1/5)^300= [(-1/5)^3]^100=(1/125)^100

(-1/3)^500=[(-1/3)^5]^100=(1/243)^100 

k mik tròn 45 nhé

So sánh : 3⁵⁰⁰ và 5³⁰⁰

3⁵⁰⁰=(3⁵)¹⁰⁰=243¹⁰⁰

5³⁰⁰=(5³)¹⁰⁰=125¹⁰⁰

Vì 243¹⁰⁰ > 125¹⁰⁰

Nên 3⁵⁰⁰ > 5³⁰⁰

5^300=(5^3)^100=125^100

3^500=(3^5)^100=243^100

Vì 125<243 nên 125^100<243^100

Vậy 125^100<243^100

tk cho mk nha bn

\(5^{300}=5^{3.100}=125^{100}\)

\(3^{500}=3^{5.100}=243^{100}\)

vì 125<243 nên \(5^{300}< 3^{500}\)

chết mk nhầm, phải là 5^300>3^500 chứ, sorry nhìu nha

So sánh : 3⁵⁰⁰ và 5³⁰⁰

3⁵⁰⁰=(3⁵)¹⁰⁰=243¹⁰⁰

5³⁰⁰=(5³)¹⁰⁰=125¹⁰⁰

Vì 243¹⁰⁰ > 125¹⁰⁰

Nên 3⁵⁰⁰ > 5³⁰⁰

3⁵⁰⁰=(3⁵)¹⁰⁰=243¹⁰⁰

5³⁰⁰=(5³)¹⁰⁰=125¹⁰⁰

vay 3⁵⁰⁰>5³⁰⁰

So sánh 3⁵⁰⁰ và 5³⁰⁰

Ta có :3⁵⁰⁰=(3⁵)¹⁰⁰=243¹⁰⁰

5³⁰⁰=(5³)¹⁰⁰=125¹⁰⁰

Vì 243¹⁰⁰ > 125¹⁰⁰

Nên 3⁵⁰⁰ > 5³⁰⁰

a.

\(3^{200}=\left(3^2\right)^{100}=9^{100}>8^{100}=\left(2^3\right)^{100}=2^{300}\)

Vậy \(3^{200}>2^{300}\)

b.

\(5^{200}=\left(5^2\right)^{100}=25^{100}< 32^{100}=\left(2^5\right)^{100}=2^{500}\)

Vậy \(5^{200}< 2^{500}\)

Ta có : \(3^{200}=3^{2.100}=\left(3^2\right)^{100}=9^{100}\)

\(2^{300}=2^{3.100}=\left(2^3\right)^{100}=8^{100}\)

\(\Rightarrow9^{100}>8^{100}\)

\(\Rightarrow3^{200}>2^{300}\)

Ta có : \(5^{200}=5^{2.100}=\left(5^2\right)^{100}=25^{100}\)

\(2^{500}=2^{5.100}=\left(2^5\right)^{100}=32^{100}\)

\(\Rightarrow25^{100}< 32^{100}\)

\(\Rightarrow5^{200}< 2^{500}\)

4 = 2^2 => 4 ^a =2^2a 

mà 2222*2 =4444 => 2^4444=4^2222

a hai cái bằng nhau

b 3 ^ 500 lớn hơn

a)Ta có :  \(4^{2222}\) \(=4^{2.1111}=\left(4^2\right)^{1111}=16^{1111}\)

\(2^{4444}=2^{4.1111}=\left(2^4\right)^{1111}=16^{1111}\)

Vì \(16^{1111}=16^{1111}\Rightarrow4^{2222}=2^{4444}\)

b) Ta có : \(5^{300}=5^{3.100}=\left(5^3\right)^{100}=125^{100}\)

\(3^{500}=3^{5.100}=\left(3^5\right)^{100}=243^{100}\)

Vì \(125^{100}< 243^{100}\Rightarrow5^{300}< 3^{500}\)

\(3^{500}=\left(3^5\right)^{100}=243^{100}\)

\(7^{300}=\left(7^3\right)^{100}=343^{100}\)

Ta thấy:\(243^{100}< 343^{100}\)

\(=>3^{500}< 7^{300}\)

7^300 = 7^(3.100) =(7^3)^100 =343^100

         3^500 = 3^(5.100) = (3^5)^100 = 243^100

Vì 343^100 > 243^100 Vậy 7^300 > 3^500

a) Ta có \(5^{300}=5^{3.100}=\left(5^3\right)^{100}=125^{100}\)

\(3^{500}=3^{5.100}=\left(3^5\right)^{100}=243^{100}\)

Vì 125 < 243 nên \(125^{100}< 243^{100}\)

Vậy \(5^{300}< 3^{500}\)

b) Ta có \(2^{15}=2^{13+2}=2^{13}.2^2=4.2^{13}\)

Vì 4<7 nên \(4.2^{13}< 7.2^{13}\)

Vậy \(2^{15}< 7.2^{13}\)

\(a)\)\(5^{300}=\left(5^3\right)^{100}=125^{100}\)

\(3^{500}=\left(3^5\right)^{100}=243^{100}\)

Vì \(125^{100}< 243^{100}\) nên \(5^{300}< 3^{500}\)

Vậy \(5^{300}< 3^{500}\)

\(b)\)\(2^{15}=2^{13+2}=2^{13}.2^2=4.2^{13}< 7.2^{13}\)

Vậy \(7.2^{13}>2^{15}\)

Chúc bạn học tốt ~ 

a) Ta có:

\(2^{300}=2^{3\cdot100}=\left(2^3\right)^{100}=8^{100}\)

\(3^{200}=3^{2\cdot100}=\left(3^2\right)^{100}=9^{100}\)

Mà: \(8< 9\)

\(\Rightarrow8^{100}< 9^{100}\)

\(\Rightarrow2^{300}< 3^{200}\)

b) Ta có:

\(3^{500}=3^{5\cdot100}=\left(3^5\right)^{100}=243^{100}\)

\(7^{300}=7^{3\cdot100}=\left(7^3\right)^{100}=343^{100}\)

Mà: \(243< 343\)

\(\Rightarrow243^{100}< 343^{100}\)

\(\Rightarrow3^{500}< 7^{300}\)

c) Ta có: 

\(8^5=\left(2^3\right)^5=2^{3\cdot5}=2^{15}=2\cdot2^{15}\)

\(3\cdot4^7=3\cdot\left(2^2\right)^7=3\cdot2^{2\cdot7}=3\cdot2^{14}\)

Mà: \(2< 3\)

\(\Rightarrow2\cdot2^{14}< 3\cdot2^{14}\)

\(\Rightarrow8^5< 3\cdot4^7\)

d) Ta có:

\(202^{303}=202^{3\cdot101}=\left(202^3\right)^{101}=8242408^{101}\)

\(303^{202}=303^{2\cdot101}=\left(303^2\right)^{101}=91809^{101}\)

Mà: \(8242408>91809\)

\(\Rightarrow8242408^{101}>91809^{101}\)

\(\Rightarrow202^{303}>303^{202}\)