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: \(8242408>91809\)

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

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

a ) 2²⁰⁰<8³⁰⁰

b ) 25²⁰⁰>5³⁰⁰

c ) 4²¹<64⁷

a)\(8^{300}=\left(2^3\right)^{300}=2^{900}\)

Vì \(200< 900\Rightarrow2^{200}< 8^{300}\)

b)\(25^{200}=\left(5^2\right)^{200}=5^{400}\)

Vì \(400>300\Rightarrow25^{200}>5^{300}\)

c)\(64^7=\left(4^3\right)^7=4^{21}\)

Vì \(4^{21}=4^{21}\Rightarrow4^{21}=64^7\)

a,3²⁰ và 27⁴

3²⁰=(3⁵)⁴=243⁴>27⁴

Vậy 3²⁰>27⁴

b,5³⁴ và 25x5³⁰

25x5³⁰=5²x5³⁰=5³²<5³⁴

=>5³⁴>25x5³⁰.

c,2²⁴và 26⁶

2²⁴=(2⁴)⁶=16⁶<26⁶

=>2²⁴<26⁶

d,10³⁰và 4⁵⁰

10³⁰=(10³)¹⁰=1000¹⁰

4⁵⁰=(4⁵)¹⁰=1024¹⁰

Vì 1000¹⁰<1024¹⁰nên 10³⁰<4⁵⁰.

e,2³⁰⁰và 3²⁰⁰

2³⁰⁰=(2³)¹⁰⁰=8¹⁰⁰

3²⁰⁰=(3²)¹⁰⁰=9¹⁰⁰

Vì 8¹⁰⁰<9¹⁰⁰ nên 2³⁰⁰<3²⁰⁰

bài quen quen

Có: 3²⁰⁰=(3²)¹⁰⁰=9¹⁰⁰

      2³⁰⁰=(2³)¹⁰⁰=8¹⁰⁰

=>9¹⁰⁰>8¹⁰⁰

<=>3²⁰⁰>2³⁰⁰

Vậy....

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

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

Vì\(8< 9\Rightarrow8^{100}< 9^{100}\Leftrightarrow2^{300}< 3^{200}\)

em khong biet thua chi chi hay ra toan lop 4 di chi

2³⁰⁰ = ( 2³)¹⁰⁰ = 8¹⁰⁰

3²⁰⁰ = ( 3²)¹⁰⁰ = 9¹⁰⁰

vậy 8 mũ 100 < 9 mũ 100

nên 2 mũ 300 < 3 mũ 200

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

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

mà \(9^{100}>8^{100}\Rightarrow3^{200}>2^{300}\)

Vậy,.........

a) <

b) =

c) =

d) =

e) =

f) =

 \(I-2I^{300}vàI-4I^{500}\)

ta có I -2I ^300 = 2^300

I-4I^500= 4^500= 2^2^500= 2^1000

vậy I-4I mũ 500 lớn hơn

đó là câu mấy vậy THÙY dương