On the powerful numbers in $\prod_{x=g}^{f}(x^k\pm h^k)$

When $k$ is odd with at most $t$ distinct prime factors, for $Q=\frac{1}{2}$ and positive integers $f,g,h$ belonging to some specific sequences, results from the literature indicate that there are constants $C(Q,t)$ such that $C=\prod_{x=g}^{f}(x^k+h^k)$ is not a powerful number if $f+h\geq\max\{C(Q,t),\frac{1}{Q}(g+h-1)\}$. When $k$ is odd, it is proved that $C$ is not a powerful number if $f+h\geq\max\{10^6,\frac{1}{Q}(g+h-1)\}$ for any $f,g,h$ and any $Q\in[0.5,0.89963]$. Similar conclusions on $D=\prod_{x=g}^{f}(x^k-h^k)$ are also proved.