Question

So sánh 

a ) 2²²⁵và 3¹⁵⁰

b) 2⁹¹ và 5³⁵ 

c) 99²⁰ và 9999¹⁰

Answer 1

\(2^{225}=8^{75}< 9^{75}=3^{150}\)

\(2^{91}>2^{90}=32^{18}>25^{18}=5^{36}>5^{35}\)

\(99^{20}=\left(99.99\right)^{10}< \left(99.101\right)^{10}=9999^{10}\)

Answer 2

a, \(2^{225}=\left(2^3\right)^{75}\) 

    \(3^{150}=\left(3^2\right)^{75}\)

b,\(2^{91}=\left(2^{13}\right)^7\)

\(5^{35}=\left(5^5\right)^7\)

c,\(99^{20}=\left(99\cdot99\right)^{10}\)

\(9999^{10}=\left(99\cdot101\right)^{10}\)

Answer 3

a, 2²²⁵ = ( 2³ )⁷⁵ = 8⁷⁵

3¹⁵⁰ = ( 3² )⁷⁵ = 9⁷⁵

Vì 8⁷⁵ < 9¹⁵

=> 2²²⁵ < 3¹⁵⁰

Vậy ...

b, 2⁹¹ > 2⁹⁰ 

Mà 2⁹⁰ = 32¹⁸ và 32¹⁸ > 25¹⁸

25 ¹⁸ = 5³⁶ và 5³⁶ > 5³⁵

=> 2⁹¹ > 2⁹⁰ > 25¹⁸ > 5³⁵

=> 2⁹¹ > 5³⁵

Vậy ...

c, 99²⁰ = ( 99² )¹⁰ = 9801¹⁰

Mà 9801 < 9999 

=> 9801¹⁰ < 9999¹⁰

=> 99²⁰ < 9999¹⁰

Vậy ...

Hok tốt