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 \(729^3< 9^{21}\)