a, 24^10 < 3^30 + 4^30 + 5^30

b, 2^100 < 5^50 < 3^75.

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

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

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

Vì:     \(16^{25}< 25^{25}< 27^{25}\Rightarrow2^{100}< 5^{50}< 3^{75}\Rightarrow a< c< b\)

tíc mình nha

so sánh các số a,b,c 

a=2¹⁰⁰

b=3⁷⁵

c=5⁵⁰

 \(=2^{100}=\left(2^{20}\right)^5\)

\(3^{75}=\left(3^{15}\right)^5\)

\(5^{50}=\left(5^{10}\right)^5\)

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

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

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

Vì: \(16^{25}< 25^{25}< 27^{25}\Rightarrow2^{100}< 5^{50}< 3^{75}\Rightarrow a< c< b\)

Ta có :

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

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

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

Do \(16^{25}< 25^{25}< 27^{25}\)

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

1/ a = 2¹⁰⁰ = (2⁴)²⁵ = 16²⁵

b = 3⁷⁵ = (3³)²⁵ = 27²⁵

c = 5⁵⁰ = (5²)²⁵ = 25²⁵

Do: 16 < 25 < 27  => 16²⁵ < 25²⁵ < 27²⁵  => 2¹⁰⁰ < 5⁵⁰ < 3⁷⁵  => a < c < b

thank nhìu :3

Bài 1:

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

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

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

Ta có: \(2^4< 5^2< 3^3\left(16< 25< 27\right)\) nên \(a< c< b\)

chịu thua

a) Ta có: 3³⁹<3⁴⁰=(3⁴)¹⁰=81¹⁰

11²¹>11²⁰=(11²)¹⁰=121¹⁰

Mà 121^10>81^10=>11^21>3^39

a) \(2^{135}=2^{3.45}=\left(2^3\right)^{45}=8^{45}\)
\(3^{90}=3^{2.45}=\left(3^2\right)^{45}=9^{45}\)
Vì \(8^{45}< 9^{45}\)nên \(2^{135}< 3^{90}\)

b) \(4^{75}=4^{3.25}=\left(4^3\right)^{25}=64^{25}\)
\(3^{100}=3^{4.25}=\left(3^4\right)^{25}=81^{25}\)
Vì \(64^{25}< 81^{25}\)nên \(4^{75}< 3^{100}\)

c) \(4^{100}=4^{4.25}=\left(4^4\right)^{25}=256^{25}\)
\(9^{75}=9^{3.25}=\left(9^3\right)^{25}=729^{25}\)
Vì \(256^{25}< 729^{25}\)nên \(^{4^{100}< 9^{75}}\)

chtt