\(\frac{2}{3}< \frac{5}{7}\)                                               

\(\frac{49}{15}>\frac{75}{41}\)    

Ai tích mik mik sẽ tích lại nha !                                                     

Không quy đòng mình so sánh bằng cách chia tự và mẫu

2/3 = 0,(6)

5/7 = 0,(714285)

=> 2/3 < 5,7

49/15 = 3,2(6)

75/41= 1,(82926)

=> 49/15 > 75/41

\(\frac{2}{3}< \frac{5}{7}\)

(105)^25.2  = 11025²⁵

(73)^3.25= 389017²⁵

=>107⁵⁰<73⁷⁵

 - \(\dfrac{3}{19}\) < 0 < \(\dfrac{5}{27}\) < \(\dfrac{5}{27}\)

vậy - \(\dfrac{3}{19}\) < \(\dfrac{5}{27}\)

3⁷⁵=(3³)²⁵=27²⁵>25²⁵=(5²)²⁵=5⁵⁰

vậy 3⁷⁵>5⁵⁰

Ta có 3^75 = (3^3)^25= 9^25

5^50 = (5^2)^25 =-10^25

=) 9<10 =) 3^75 < 5^50

3⁷⁵  > 3⁵⁰

\(\text{Ta có}:\)

\(3^{75}=\left(3^3\right)^{25}\)

\(5^{50}=\left(5^2\right)^{25}\)

\(\Rightarrow\left(3^3\right)^{25}=27^{25}\)

\(\Rightarrow\left(5^2\right)^{25}=25^{25}\)

\(\text{Vậy }27^{25}>25^{25}\)

\(\Rightarrow3^{75}>5^{50}\)

\(3^{40}=\left(3^4\right)^{10}=81^{10}\)

\(4^{30}=\left(4^3\right)^{10}=64^{10}\)

Vì \(81>64\)

`-> 81^10 > 64^10`

`-> 3^40 > 4^30`

`----`

`2^75=(2^3)^25=8^25`

`3^50=(3^2)^25=9^25`

Vì `9>8`

`-> 9^25 > 8^25`

`-> 3^50 > 2^75`.

a: 3^40=81^10

4^30=64^10

=>3^40>4^30

b: 2^75=8^25

3^50=9^25

=>2^75<3^50

\(a=2^{100}=\left(2^4\right)^{25}=16^{25}\)

\(b=3^{75}=\left(3^3\right)^{25}=27^{25}\)

\(c=5^{50}=\left(5^2\right)^{25}=25^{25}\)

Vì \(16^{25}< 25^{25}< 27^{25}\)

\(\Rightarrow a< c< b\)

\(a=2^{100},b=3^{75},c=5^{50}\\ \Rightarrow a=30^{85},b=30^{65},c=30^{44}\\ \Rightarrow a>b>c\)

Ta có:

\(a=2^{100}=2^{4\cdot25}=\left(2^4\right)^{25}=16^{25}\)

\(b=3^{75}=3^{3\cdot25}=\left(3^3\right)^{25}=27^{25}\)

\(c=5^{50}=5^{2\cdot25}=\left(5^2\right)^{25}=25^{50}\)

Ta thấy: 

\(16< 25< 27\)

\(\Rightarrow16^{25}< 25^{25}< 27^{25}\)

\(\Rightarrow2^{100}< 5^{50}< 3^{75}\)

\(\Rightarrow a< c< b\)