Question

so sánh 

2⁶ và 8²; 3²⁰⁰ và 2³⁰⁰;9²⁰ và 27^13';10²⁰ và 2¹⁰⁰;13⁴⁰ và 2¹⁶¹

giải giúp mình  nha

Answer 1

+)\(8^2=\left(2^3\right)^2=2^6\)

+)\(3^{200}=3^{2.100}=\left(3^2\right)^{100}=9^{100}\)

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

Vì \(9>8\Rightarrow9^{100}>8^{100}\)hay \(3^{200}>2^{300}\)

+)\(9^{20}=\left(3^2\right)^{20}=3^{40}\)

\(27^{13}=\left(3^3\right)^{13}=3^{39}\)

Vì \(40>39\Rightarrow3^{40}>3^{39}\)hay \(9^{20}>27^{13}\)

+)\(10^{20}=10^{2.10}=\left(10^2\right)^{10}=100^{10}\)

\(2^{100}=2^{10.10}=\left(2^{10}\right)^{10}=1024^{10}\)

Vì \(100< 1024\Rightarrow100^{10}< 1024^{10}\)hay \(10^{20}< 2^{100}\)

+)\(2^{161}=2^{4.40+1}=\left(2^4\right)^{40}.2=16^{40}.2\)

Vì \(13< 16\Rightarrow13^{40}< 16^{40}\)\(\Rightarrow13^{40}< 2^{161}\)