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Let $q$ be a positive integer. Recently, Niu and Liu proved that if $n\ge\max\{q,1198-q\}$, then the product $(1^3+q^3)(2^3+q^3)\cdots (n^3+q^3)$ is nota powerful number. In this note, we prove that (i) for any odd prime power$\ell$ and $n\ge \max\{q,11-q\}$, the product$(1^{\ell}+q^{\ell})(2^{\ell}+q^{\ell})\cdots (n^{\ell}+q^{\ell})$ is not apowerful number; (2) for any positive odd integer $\ell$, there exists aninteger $N_{q,\ell}$ such that for any positive integer $n\ge N_{q,\ell}$, theproduct $(1^{\ell}+q^{\ell})(2^{\ell}+q^{\ell})\cdots (n^{\ell}+q^{\ell})$ isnot a powerful number.

Powerful numbers in $(1^{\ell}+q^{\ell})(2^{\ell}+q^{\ell})\cdots (n^{\ell}+q^{\ell})$