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17²⁰ =(17⁴)⁵ = 83521⁵

31¹⁵ = (31³)⁵ = 29791⁵

Vì 83521 > 29791 => 17²⁰ > 31¹⁵

\(17^{20}=\left(17^4\right)^5=83521^5\)

\(31^{15}=\left(31^3\right)^5=29719^5\)

Vậy: \(17^{20}>31^{15}\)

17²⁰ > 16²⁰ = 16⁵ . 16¹⁵ = (2⁴)⁵ . 16¹⁵ = 2²⁰ . 16¹⁵ > 2¹⁵ . 16¹⁵ = 32¹⁵ > 31¹⁵​

Ta có:

\(17^{20}=\left(17^4\right)^5=83521^5\)

\(31^{15}=\left(31^3\right)^5=29791^5\)

Vì 83521>29791 \(\Rightarrow17^{20}>31^{15}\)

Ta có :

17²⁰ > 16²⁰ = ( 2⁴ )²⁰ = 2⁸⁰

31¹⁵ < 32¹⁵ = ( 2⁵ )¹⁵ = 2⁷⁵

Mà 31¹⁵ < 32¹⁵ < 16²⁰ < 17²⁰ => 31¹⁵ < 17²⁰

Ta có : 

\(17^{20}>16^{20}=\left(2^4\right)^{20}=2^{80}\)

\(31^{15}< 32^{15}=\left(2^5\right)^{15}=2^{75}\)

Vì \(2^{80}>2^{75}\) nên \(17^{20}>31^{15}\)

Vậy \(17^{20}>31^{15}\)

Chúc bạn học tốt ~ 

a)=

b)>

c)=

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/

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

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

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

\(31^{15}< 32^{15}=\left(2^5\right)^{15}=2^{75}\)

\(17^{19}>16^{19}=\left(2^4\right)^{19}=2^{76}\)

Do \(2^{75}< 2^{76}\Rightarrow31^{15}< 2^{75}< 2^{76}< 17^{19}\)

Vậy \(31^{15}< 17^{19}\)

17/15 và 31/29

17/15 - 1 = 2/15 ;  31/29 - 1 = 2/29

so sánh 2/15 và 2/29 ta có 2/15 > 2/29 nên 17/15 > 31/29

12/13 và 22/33

1 - 12/13 = 1/13   ;    1 - 22/33 = 1/33

so sánh 1/13 và 1/33 ta có 1/13 > 1/33 nên 12/13 < 22/33

chúc bn hok tốt!