Question

giúp mình với

bài 2 so sánh 99²⁰và 9999¹⁰

Answer 1

Ta có:

\(99^{20}=\left(99^2\right)^{10}=\left(99.99\right)^{10}\)

\(9999^{10}=\left(99.101\right)^{10}\)

Vì \(99.99< 99.101\) \(\Rightarrow\left(99.99\right)^{10}< \left(99.101\right)^{10}\Leftrightarrow99^{20}< 9999^{10}\)

Answer 2

\(\left\{{}\begin{matrix}99^{20}=\left(99^2\right)^{10}\\\left(9999\right)^{10}=\left(99.101\right)^{10}\end{matrix}\right.\)

\(99^2< 99.101\Leftrightarrow\left(99^2\right)^{10}< \left(99.101\right)^{10}\)

\(\Leftrightarrow99^{20}< 9999^{10}\Rightarrowđpcm\)