Question

So sánh \(2^{300}+3^{300}+4^{300}\) và  \(729.24^{100}\)

Answer 1

\(729.24^{100}=3^6.\left(2^3.3\right)^{100}=3^{106}.2^{300}\)

\(4^{300}=2^{300}.2^{300}\)

Ta có: \(2^{300}>2^{212}=\left(2^2\right)^{106}=4^{106}>3^{106}\)

\(\Rightarrow2^{300}.2^{300}>2^{300}.3^{106}\Rightarrow4^{300}>729.24^{100}\)

Vậy \(2^{300}+3^{300}+4^{300}>729.24^{100}\)