\(26^{14}>25^{14}=\left(5^2\right)^{14}=5^{28}\)

\(5^{30}=\left(5^3\right)^{10}=125^{10}>124^{10}\)

\(4^{21}=\left(4^3\right)^7=64^7>64^2\)

\(27^{16}.16^9=\left(3^3\right)^{16}.\left(4^2\right)^9=3^{48}.4^{18}>12^{18}=3^{18}.4^{18}\)

\(31^{11}16^{14}=\left(2^4\right)^{14}=2^{56}\)

\(2^{56}>2^{55}\) => \(17^{14}>31^{11}\)

Các bài khác làm tương tự

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

\(31^{11}>22^{11}=2^{11}.11^{11}>11^3.11^{11}=11^{14}\)

31¹¹<32¹¹=(2⁵)¹¹=2⁵⁵

=>31¹¹<2⁵⁵

17¹⁴>16¹⁴=(2⁴)¹⁴=2⁵⁶

=>17¹⁴>2⁵⁶

=>31¹¹<2⁵⁵<2⁵⁶<17¹⁴

=>31¹¹<17¹⁴

Ta có : 

31 < 32 = 2⁵

=> 31¹¹ < ( 2⁵ )¹¹ = 2⁵⁵

17 > 16 = 2⁴

17¹⁴ > (2⁴ )¹⁴ = 2⁵⁶

Vì 55 < 56 nên 2⁵⁵ < 2⁵⁶

31¹¹ < 2⁵⁵ < 2⁵⁶ < 17¹⁴

=> 31¹¹ < 17¹⁴

31¹¹<32¹¹=(2⁵)¹¹=2⁵⁵

=>31¹¹<2⁵⁵

17¹⁴>16¹⁴=(2⁴)¹⁴=2⁵⁶

17¹⁴>2⁵⁶

vì 2⁵⁵<2⁵⁶ nên

31¹¹<2⁵⁵<2⁵⁶<17¹⁴

vậy 31¹¹<17¹⁴

31^11 và 17^14

Ta có:31^11<32^11=(2^5)^11=2^55

         17^14>16^14=(2^4)^14=2^56

=>31^11<2^55<2^56<17^14

=>31^11<17^14

Vậy 31^11<17^14

31^11<17<14