Question

So sánh 9²⁵ và 4⁴⁰

Answer 1

\(9^{25}=\left(9^5\right)^5\)

\(4^{40}=\left(4^8\right)^5\)\(=\left(16^7\right)^5\)

\(\Rightarrow9^{25}< 4^{40}\)

Answer 2

9²⁵=(3²)²⁵=3⁵⁰=(3⁵)¹⁰=243¹⁰

4⁴⁰=(4⁴)¹⁰=256¹⁰

Vì 243¹⁰<256¹⁰ nên 9²⁵<4⁴⁰

Answer 3

ta có :

9²⁵ = ( 3² ) ²⁵ = 3^{2 . 25} = 3⁵⁰ = 3^{5 . 10} = ( 3⁵ ) ¹⁰ = 243¹⁰

4⁴⁰ = 4^{4 . 10} = ( 4⁴ ) ¹⁰ = 256¹⁰

Vì 243 < 256 nên 243¹⁰ < 256¹⁰ hay 9²⁵ < 4⁴⁰