If $(ab)^{3}=a^{3}b^{3}$ and $(ab)^{5}=a^{5}b^{5}$ for all $a,b \in G$ then $G$ 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.
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