The balanced chemical equation for the reaction between barium nitrate (Ba(NO₃)₂) and potassium hydroxide (KOH) is:

Ba(NO₃)₂(aq) + 2KOH(aq) → Ba(OH)₂(s) + 2KNO₃(aq)

Here's the breakdown:

* Ba(NO₃)₂(aq): Barium nitrate, dissolved in water (aqueous).

* KOH(aq): Potassium hydroxide, dissolved in water (aqueous).

* Ba(OH)₂(s): Barium hydroxide, a solid precipitate.

* KNO₃(aq): Potassium nitrate, dissolved in water (aqueous).

Explanation:

This reaction is a double displacement reaction. Barium nitrate and potassium hydroxide react to form barium hydroxide and potassium nitrate. Barium hydroxide is a white solid that is insoluble in water and precipitates out of the solution.

The equation is balanced by ensuring that the number of atoms of each element is the same on both sides of the equation. In this case, there are:

* 1 Ba atom on each side

* 2 N atoms on each side

* 6 O atoms on each side

* 2 K atoms on each side

* 2 H atoms on each side