Let $(G,*)$ be a group with $(a*b)^3=a^3*b^3$ and $(a*b)^5=a^5*b^5\forall a,b∈G$. Show that $(G,*)$ is abelian.
Let $G$ be a group, where $(ab)^3=a^3b^3$ and $(ab)^5=a^5b^5$. Prove that $G $ is an abelian group.