1. Identify the possible ionic compounds:

* Ba²⁺ + CO₃²⁻ → BaCO₃ (Barium carbonate)

* Na⁺ + OH⁻ → NaOH (Sodium hydroxide)

2. Consider solubility rules:

* Carbonates (CO₃²⁻) are generally insoluble, except for those of Group 1 cations (like Na⁺) and ammonium (NH₄⁺).

* Hydroxides (OH⁻) are generally insoluble, except for those of Group 1 cations and some Group 2 cations (like Ba²⁺).

3. Determine the precipitate:

Since barium carbonate (BaCO₃) is insoluble according to the solubility rules, it is the most likely precipitate to form. Sodium hydroxide (NaOH) is soluble.

Therefore, the precipitate most likely to form is Barium carbonate (BaCO₃).