Question

so sánh: (-333)⁴⁴⁴ và 444³³³

Answer 1

\(\left(-333\right)^{444}=333^{444}=\text{ }\left(3\cdot111\right)^{4\cdot111}=\left(3^4\right)^{111}\cdot\left(111^4\right)^{111}=81^{111}\cdot111^{444}\)

\(444^{333}=\left(4\cdot111\right)^{3\cdot111}=\left(4^3\right)^{111}\cdot\left(111^3\right)^{111}=64^{111}\cdot111^{333}\)

\(\left\{{}\begin{matrix}81^{111}>64^{111}\\111^{444}>111^{333}\end{matrix}\right.\Rightarrow333^{444}>444^{333}\)