Question

[Thu Huyền Chu Văn An]

So sánh

a) \(3^{600}\) và \(4^{400}\)

b)\(4^{32}\) và \(16^{15}\)

Answer 1

[Phúc Trần]

a/ \(3^{600}=\left(3^3\right)^{200}=\left(27\right)^{200}\)

\(4^{400}=\left(4^2\right)^{200}=\left(16\right)^{200}\)

\(\Leftrightarrow3^{600}>4^{400}\)

b/ \(4^{32}\)

\(16^{15}=\left(4^2\right)^{15}=4^{30}\)

\(\Leftrightarrow4^{32}>16^{15}\)

Answer 2

[Nguyễn Thị Bích Thủy]

a)\(3^{600}\) = \(\left(3^3\right)^{200}\) = \(27^{200}\)
\(4^{400}\) = \(\left(4^2\right)^{200}\) = \(16^{200}\)
Vì \(27>16\Rightarrow27^{200}>16^{200}=3^{600}>4^{400}\)

Vậy\(3^{600}>4^{400}\)
b) \(32^{10}=\left(2^5\right)^{10}=2^{50} \)
\(16^{15}=\left(2^4\right)^{15}=2^{60}\)
Vì \(50< 60\Rightarrow2^{50}< 2^{60}\Rightarrow32^{10}< 16^{15}\)
Vậy\(32^{10}< 16^{15}\)