\(31^{11}< 32^{11}=2^{55}\)

\(17^{14}>16^{14}=2^{56}>2^{55}>3^{11}\)

\(\Rightarrow17^{14}>3^{11}\)

31¹¹ < 34¹¹ = 17¹¹ . 2¹¹

17¹⁴ = 17¹¹ . 17³ > 17¹¹ . 16³ = 17¹¹ . (2⁴)³ = 17¹¹ . 2¹²

Do 17¹⁴ > 17¹¹ . 2¹² > 17¹¹ . 2¹¹ > 31¹¹

=> 17¹⁴ > 31¹¹

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trong câu hỏi tương có nha

\(31^{11}<32^{11}=2^{55};17^{14}>16^{14}=2^{56}\rightarrow31^{11}<17^{14}\)

\(31^{11}< 32^{11}=\left(2^5\right)^{11}=2^{55}\)

\(17^{14}>16^{14}=\left(2^4\right)^{14}=2^{56}\)

\(\Rightarrow17^{14}>2^{56}>2^{55}>31^{11}\)