Question

So sánh 99^{20 và} 9999¹⁰

( x⁴)² = x¹² / x⁵

X¹⁰ = 25.x

\(\dfrac{790^4}{79^4}\)

Answer 1

\(99^{20}=\left(99^2\right)^{10}=9810^{10}\)

Mà \(9810^{10}< 9999 ^{10}=>99^{20}< 9999^{10}\)

Vậy ...............

Answer 2

\(\dfrac{790^4}{79^4}=10000\)

Answer 3

ta có 9999= 99 *101.
do đó 9999^10 = 99 ^10 * 101^10
còn 99^20 = 99^10 * 99^10
vì 99^10 < 101^10 nên 99^10 * 99^10 < 99 ^10 * 101^10 .
vậy 99^20 < 9999^10.