Question

3 ⁷⁸ x 243 ⁵² và 9 ¹⁰¹ x 27 ⁷⁸

Answer 1

3⁷⁸ x 243⁵² = 3⁷⁸ x ( 3⁵ )⁵² = 3⁷⁸ x 3²⁶⁰ = 3³³⁸

9¹⁰¹ x 27⁷⁸ = ( 3² )¹⁰¹ x ( 3³ )⁷⁸ = 3²⁰² x 3²³⁴ = 3⁴³⁶

Vì 338 < 436 

=> 3³³⁸ < 3⁴³⁶

=> 3⁷⁸ x 243⁵² < 9¹⁰¹ x 27⁷⁸

Answer 2

Ta có: 

\(3^{78}\times243^{52}=3^{78}\times\left(3^5\right)^{52}=3^{78}\times3^{260}=3^{338}\)

\(9^{101}\times27^{78}=\left(3^2\right)^{101}\times\left(3^3\right)^{78}=3^{202}\times3^{234}=3^{436}\)

Vì \(3^{338}< 3^{436}\)

\(\Rightarrow3^{338}< 3^{436}\)

\(\Rightarrow3^{78}\times243^{52}< 9^{101}\times27^{78}\left(đpcm\right)\)