Ta có: \(31^{111}< 32^{111}\) và \(17^{139}>16^{139}\)
\(\left\{\begin{matrix}32^{111}=\left(2^5\right)^{111}=2^{555}\\16^{139}=\left(2^4\right)^{139}=2^{556}\end{matrix}\right.\)
Vì \(2^{555}< 2^{556}\) nên \(17^{139}>2^{556}>31^{111}\)
\(\Rightarrow17^{139}>31^{111}\)
Vậy: \(17^{139}>31^{111}\)
