Question

So sánh

\(\left(17^5\right)^2va17^{10}\)

\(2^{60}va4^{20}\)

\(5^{45}va25^{15}\)

Answer 1

Ta có \(\left(17^5\right)^2=17^{10}\)

Vì \(17^{10}=17^{10}\Rightarrow\left(17^5\right)^2=17^{10}\)

\(2^{60}=\left(2^3\right)^{20}=8^{20}\)

Vì \(8^{20}>4^{20}\Rightarrow2^{60}>4^{20}\)

\(5^{45}=\left(5^3\right)^{15}=125^{15}\)

Vì \(125^{15}>25^{15}\Rightarrow5^{45}>25^{15}\)

Answer 2

a, Ta có : \(\left(17^5\right)^2=17^{10}\)

Vì \(17^{10}=17^{10}\Rightarrow\left(17^5\right)^2=17^{10}\)

b, Ta có \(2^{60}=\left(2^3\right)^{20}=8^{20}\)

Vì \(8^{20}>4^{20}\Rightarrow2^{60}>4^{20}\)

c, Ta có : \(5^{45}=\left(5^3\right)^{15}=125^5\)

Vì \(125^5>25^{15}\Rightarrow5^{45}>25^{15}\)