Question

[HOÀNG TRÚC NGÂN]

so sánh 8 mũ 12 với 12 mũ 8

Answer 1

[Dang Tung]

\(8^{12}=\left(8^3\right)^4=512^4\\ 12^8=\left(12^2\right)^4=144^4\\ \)

Nhận thấy: \(512^4>144^4\Rightarrow8^{12}>12^8\)

Answer 2

[HT.Phong (9A5)]

\(8^{12}=\left(2^3\right)^{12}=2^{36}\)

\(12^8=\left(2^2\cdot3\right)^8=\left(2^2\right)^8\cdot3^8\\ =2^{16}\cdot3^8< 2^{16}\cdot4^8=2^{16}\cdot\left(2^2\right)^8=2^{16}\cdot2^{16}=2^{32}< 2^{36}\) 

=> \(12^8< 8^{12}\)