2^99<2^100=(2^4)^25=16^25<17^25

5^299<5^300=(5^3)^100=125^100

3^501>3^500=(3^5)^100=243^100

=>125^100<243^100

=>5^299<3^501

\(\)\(17^{25}>16^{25}=\left(2^4\right)^{25}=2^{100}\)

\(2^{99}< 2^{100}mà17^{25}>16^{25}=2^{100}\)

\(=>2^{99}< 17^{25}\)

5²⁹⁹ và 3⁵⁰¹

5²⁹⁹<5³⁰⁰; 3⁵⁰¹>3⁵⁰⁰

5³⁰⁰=(5³)¹⁰⁰=125¹⁰⁰

3⁵⁰⁰=(3⁵)¹⁰⁰=243¹⁰⁰

Vì 243¹⁰⁰>125¹⁰⁰ nên 3⁵⁰¹>5²⁹⁹

a,

\(3^{34}=\left(3^{17}\right)^2=129140163^2\)

\(5^{20}=\left(5^{10}\right)^2=9765625^2\)

Vậy..........

Đùa chút thui

c,\(3^{23}=3^{21}.3^2=\left(3^3\right)^7.9=27^7.9\)

\(5^{15}=\)\(5^{14}.5=\left(5^2\right)^7.5=25^7.5\)

\(27^7>25^7\)và \(9>5\)

nên \(3^{23}>5^{15}\)

b,

5^299 < 5^300 = (5^2)^150 = 25^150

3^501 = (3^3)^167 = 27^167

=> 27^167 > 25^150 => 3^501 > 5^299

Bye bye

Chúc bạn học tốt

Theo dõi mik nha<3

 5^299 < 5^300 = (5^2)^150 = 25^150 

3^501 = (3^3)^167 = 27^167 

=> 27^167 > 25^150 => 3^501 > 5^299

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