\(32^9=\left(2^5\right)^9=2^{5.9}=2^{45}=2^{13}.2^{32}\)
\(18^{13}=\left(2.3^2\right)^{13}=2^{13}.\left(3^2\right)^{13}=2^{13}.3^{26}\)
\(2^{32}=2^{16.2}=\left(2^{16}\right)^2=65536^2\)
\(3^{26}=3^{13.2}=\left(3^{13}\right)^2=1594323^2\)
Vì \(65536^2< 1594323^2\)
Do đó \(2^{32}< 3^{26}\)
Nên \(2^{13}.2^{32}< 2^{13}.3^{26}\)
Vậy \(32^9< 18^{13}\)
