Có 31^11>31^4

Mà 31^4>17^4(vì 31>17)

=> 31^11>17^4

Vậy 31^11>17^4

Cơ số là 31>17,mũ là 11>4.Ko lớn hơn mới lạ

a/

2020.2021=(2019+1)(2022-1)=

=2019.2022-2019+2022-1=2019.2022+2>2019.2022

b/

\(4^7=\left(2^2\right)^7=2^{14}< 2^{15}\)

c/

\(199^{20}< 200^{20}=\left(8.25\right)^{20}=\left(2^3.5^2\right)^{20}=2^{60}.5^{40}\)

\(2000^{15}=\left(16.125\right)^{15}=\left(2^4.5^3\right)^{15}=2^{60}.5^{45}\)

\(\Rightarrow2000^{15}=2^{60}.5^{45}>2^{60}.5^{40}>199^{20}\)

d/

\(31^{31}< 32^{31}=\left(2^5\right)^{31}=2^{155}\)

\(17^{39}>16^{39}=\left(2^4\right)^{39}=2^{156}\)

\(\Rightarrow17^{39}=2^{156}>2^{155}>31^{31}\)

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

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

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

\(31^{11}<32^{11}=\left(2^5\right)^{11}=16^{11}<16^{14}<17^{14}\)

Vậy \(31^{11}<17^{14}\).

31^11  >  17^14

\(31^{11}<32^{11}=\left(2^5\right)^{11}=2^{55};17^{14}>16^{14}=\left(2^4\right)^{14}=2^{56}\)

Vì 2⁵⁵ < 2⁵⁶ nên 31¹¹ < 17¹⁴.

31¹¹ và 17¹⁴

31¹¹<32¹¹=(2⁵)¹¹=2⁵⁵

=>31¹¹<2⁵⁵

17¹⁴>16¹⁴=(2⁴)¹⁴=2⁵⁶

=>17¹⁴>2⁵⁶

=>31¹¹<2⁵⁵<2⁵⁶<17¹⁴

=>31¹¹<17¹⁴

\(31^{11}< 32^{11}=\left(2^5\right)^{11}=2^{55}< 2^{56}=\left(2^4\right)^{14}=16^{14}< 17^{14}\)

\(=>31^{11}< 17^{14}\)

Vậy........

ví dụ 16, trang 13, sách toán bồi dưỡng học sinh 6, bạn mở ra mà xem :))

Ta có:

31¹¹ < 32¹¹ = (2⁵)¹¹ = 2⁵⁵

17¹⁴ > 16¹⁴ = (2⁴)¹⁴ = 2⁵⁶

Vì 2⁵⁵ < 2⁵⁶ => 32¹¹ < 16¹⁴ => 31¹¹ < 17¹⁴

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

\(\Rightarrow31^{11}< 2^{55}\)

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

\(\Rightarrow17^{14}>2^{56}\)

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

\(\Rightarrow31^{11}< 17^{14}\)

BẠN LÀM THẾ SAI RỒI
LÀM NHƯ VẬY VÍ DỤ: 5>3: 6>2 =>> 5>6

Vì (-17)¹⁴<0(Vì có -17)

    31¹¹>0(vì hai số 31;11 là số nguyên dương)

             Suy ra:31¹¹>(-17)¹⁴

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

\(2^{55}< 2^{56}=\left(2^4\right)^{14}=16^{14}< \left(-17\right)^{14}\)

=> \(31^{11}< \left(-17\right)^{14}\)