Question

[Phuocdeptrai]

so  sánh

16¹⁹và8¹⁵

625² và 125⁶

4²¹ và 3¹⁴

729³ và 9²¹

Answer 1

[Greninja]

a) Ta có : \(16^{19}=\left(2^4\right)^{19}=2^{76}\)

                    \(8^{15}=\left(2^3\right)^{15}=2^{45}\)

mà \(76>45\)

\(\Rightarrow2^{76}>2^{45}\)

hay \(16^{19}>8^{15}\)

b) Ta có : \(625^2=\left(5^4\right)^2=5^8\)

                 \(125^6=\left(5^3\right)^6=5^{18}\)

mà \(8< 18\)

\(\Rightarrow5^8< 5^{18}\)

hay \(625^2< 125^6\)

c) Ta có : \(3^{14}< 3^{21}< 4^{21}\)

\(\Rightarrow3^{14}< 4^{21}\)

d) Ta có : \(729^3=\left(3^6\right)^3=3^{18}\)

                   \(9^{21}=\left(3^2\right)^{21}=3^{42}\)

mà \(18< 42\)

\(\Rightarrow3^{18}< 3^{42}\)

hay \(729^3< 9^{21}\)