Question

So sánh : 27²⁰⁰ và 25³⁰⁰

Answer 1

\(=27^{100.2}và25^{100.3}\)

\(=\left(27^2\right)^{100}và\left(25^3\right)^{100}\)

\(\Rightarrow729^{100}< 15625^{100}\)

Answer 2

\(=27^{100.2}\)và \(25^{100.3}\)

\(=\left(27^2\right)^{100}\)và \(\left(25^3\right)^{100}\)

\(\Rightarrow729^{100}< 15625^{100}\)

Tích nha

Answer 3

Ta có : \(27^{200}=\left(3^3\right)^{200}=3^{3.200}=3^{600}\)

          \(25^{300}=\left(5^2\right)^{300}=5^{2.300}=5^{600}\)

Vì 3 < 5 nên \(3^{600}< 5^{600}\)

Vậy \(27^{200}< 25^{300}\)

Answer 4

Ta có:\(27^{200}\)=\(27^{2.100}\)=\(\left(27^2\right)^{100}\)=\(729^{100}\)

        \(25^{300}\)=\(25^{3.100}\)=\(\left(25^3\right)^{100}\)=\(15625^{100}\)

     Vì:\(729^{100}< 15625^{100}\)nên  \(27^{200}< 25^3\)

Answer 5

ta có :

 27²⁰⁰ = 27^2.100 = (27²)¹⁰⁰ =  729¹⁰⁰

25³⁰⁰ = 25^3.100 = (25³)¹⁰⁰ = 15625¹⁰⁰

vì 729 < 15625

=> 729¹⁰⁰ < 15625¹⁰⁰

hay 27²⁰⁰ < 25³⁰⁰

Answer 6

\(27^{200}=27^{100.2}\) =  \(\left(27^2\right)^{100}=729^{100}\)

\(25^{300}=25^{100.3}\)=  \(\left(25^3\right)^{100}=15625^{100}\)

=>  \(729^{100}< 15625^{100}\)=> \(27^{200}< 25^{300}\)