Question

So sánh:

a, 2\(^{91}\) và 5\(^{35}\)

b, 222\(^{333}\) và 333\(^{222}\)

Answer 1

a, \(2^{91}\) và \(5^{35}\)

Ta có :

\(2^{91}=\left(2^{13}\right)^7=8192^7\)

\(5^{35}=\left(5^5\right)^7=3125^7\)

Vì \(8192>3125\) nên \(2^{91}>5^{35}\)

b, \(222^{333}\) và \(333^{222}\)

Ta có :

\(222^{333}=\left(2.111\right)^{333}=2^{333}.111^{333}=\left(2^3\right)^{111}.111^{333}=8^{111}.111^{333}\)

\(333^{222}=\left(3.111\right)^{222}=3^{222}.111^{222}=\left(3^2\right)^{111}.111^{222}=9^{111}.111^{222}\)

Vì \(8^{111}< 9^{111}\) nên \(222^{333}< 333^{222}\)