\(3.24^{100}=3.3^{100}.8^{100}=3^{101}.\left(2^3\right)^{100}=3^{101}.2^{3.100}=3^{101}.2^{300}\)
\(4^{300}=2^{300}.2^{300}=2^{2.150}.2^{300}=\left(2^2\right)^{150}.2^{300}=4^{150}.2^{300}\)
Vì\(3^{101}.2^{300}< 4^{150}.2^{300}\)nên \(3.24^{100}< 4^{300}\Rightarrow3.24^{100}< 3^{300}+4^{300}\)

KHÙNG

dáp án

<

ht

ta co: 3³⁰⁰ =(3³)¹⁰⁰ =27¹⁰⁰

             4³⁰⁰=(4³)¹⁰⁰=64¹⁰⁰

Vi 3.24<27<64 nen 3.24¹⁰⁰<3³⁰⁰<4³⁰⁰

\(3^{300}+4^{300}\)

\(=27^{100}.64^{100}\)

\(=1728^{100}>3.24^{100}\)

Lớn hơn nhé !

Ta có :

\(3.24^{100}=3.3^{100}.8^{100}=3^{101}.8^{100}\)

Xét : \(4^{300}\)và \(3^{101}.8^{100}\)ta có : 

\(4^{300}=2^{300}.2^{300}=\left(2^2\right)^{150}.\left(2^3\right)^{100}=\)\(4^{150}.8^{100}\)

Vì \(8^{100}=8^{100}\)và \(4^{150}>3^{101}\Rightarrow4^{300}>3^{101}.8^{100}\)

\(\Rightarrow4^{300}+3^{400}>3.24^{100}\)

3x24^100=(2x3x4)^100 
=3x(3^100)x4^150 
xet 4^300-3x24^100= 
4^300-3x(3^100)x4^150= 
(4^150)(4^150-3x3^100)> 
(4^150)(3^150-3x3^100)> 
(4^150)(3^100)(3^50-3)>0 

==>.....