Question

So sánh các cặp số sau;

a,A=27⁵ và B=243³

b,A=2³⁰⁰ và B=3²⁰⁰

Answer 1

Ta có 27^5=3^3^5=3^15
243^3=3^5^3=3^15
Vậy A=B
2^300=2^(3.100)=2^3^100=8^100
3^200=3^(2.100)=3^2^100=9^100
Vậy A<B

Answer 2

\(a,A=27^5\)và \(B=243^3\)

Ta xét :

\(A=27^5=\left(3^3\right)^5=3^{15}\)

\(B=243^3=\left(3^5\right)^3=3^{15}\)

Mà \(3^{15}=3^{15}\)

\(\Rightarrow A=B\)

\(b,A=2^{300}\)và \(B=3^{200}\)

Ta xét :

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

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

Mà \(9^{100}>8^{100}\)

\(\Rightarrow B>A\)

Answer 3

a)  \(27^5\)=   \(\left(3^3\right)^5\)=   \(3^{15}\)

\(243^3\)=   \(\left(3^5\right)^3\)=   \(3^{15}\)

Vì   \(3^{15}\)=   \(3^{15}\)

\(\Rightarrow\)..................................

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

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

Vì   \(9^{100}\)>   \(8^{100}\)

\(\Rightarrow\).............................................