I have a question about the book A Guide to Quantum Groups written by Vyjayanthi Chari and Andrew Pressley. It comes from section $9.3$ on page $300$ of this book

In Section 9.1, the authors define the algebra $U_q(\mathfrak{g})$ over $\mathbb{Q}(q)$ where $\mathfrak{g}$ is a finite-dimensional complex Lie algebra. Let $\mathbb{A} =\mathbb{Z}[q,q^{-1}]$, they define $U^{res}_{\mathbb{A} }$ and $U^{res}_{\varepsilon}=U^{res}_{\mathbb{A} }\otimes_{\mathbb{A} }\mathbb{Q}(\varepsilon)$. Here $\varepsilon $ is a primitive $\ell$th root of unity, where $\ell$ is odd and greater than $d_i$ for all $i$.

Let $$\left[ \begin{array}{c} K_i;0\\ s\\ \end{array} \right] _{q_i}=\prod_{r=1}^{s}{\frac{K_iq^{1-r}-{K_i}^{-1}q^{r-1}}{q_{i}^{r}-q_{i}^{-r}}}.$$ Then in page $300$ remark $[1]$, the author write an element $\left[ \begin{array}{c} K_i;0\\ \ell\\ \end{array} \right] _{\varepsilon _i}\in U_\varepsilon^{res}$ .

Here is my question:

If I replace $q_i$ with $\varepsilon_i$, because $\varepsilon^l=\varepsilon^{-l}=1$, then there will have $0$ in the denominator.

So I am very confused about it. How should I deal with $\left[ \begin{array}{c} K_i;0\\ \ell\\ \end{array} \right] _{\varepsilon _i}$?

Any help and references are greatly appreciated.

Thanks!