Yes, a precipitate does form when zinc nitrate (\( \text{Zn(NO}_3\text{)}_2 \)) and ammonium sulfide (\( \text{(NH}_4\text{)}_2\text{S} \)) are mixed. The reaction can be represented as follows:
\[ \text{Zn(NO}_3\text{)}_2 + \text{(NH}_4\text{)}_2\text{S} \rightarrow \text{ZnS} \downarrow + 2 \text{NH}_4\text{NO}_3 \]
In this reaction, zinc sulfide (\( \text{ZnS} \)) forms as a solid precipitate. The empirical formula of the precipitate is \( \text{ZnS} \).