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

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

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

31¹¹ < 34¹¹ = 17¹¹ . 2¹¹

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

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

=> 17¹⁴ > 31¹¹

☆★☆★☆

31<32=2⁵

31¹¹< (2⁵)¹¹ =2⁵⁵

17>16=2⁴

17¹⁴>(2⁴)¹⁴=2⁵⁶

55<56=>2⁵⁵<2⁵⁶

=>31¹¹<17¹⁴

Ta có:

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

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

\(Vì\) \(2^{55}< 2^{56}\Rightarrow31^{11}< 17^{14}\)

\(Vậy\)\(31^{11}< 17^{14}\)

trong câu hỏi tương có nha

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

Ta có :

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

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

Mà 2⁵⁵ < 2⁵⁶ nên ta được 31¹¹ < 2⁵⁵ < 2⁵⁶ < 17¹⁴

Vậy 31¹¹ < 17¹⁴

Chọn mình nha !!!cảm ơn

\(\hept{\begin{cases}31^{11}< 32^{11}=\left(2^5\right)^{11}=2^{55}\\17^{14}>16^{14}=\left(2^4\right)^{14}=2^{56}\end{cases}}\Rightarrow31^{11}< 2^{55}< 2^{56}< 17^{14}\Rightarrow31^{11}< 17^{14}\)