The balanced chemical equation for the reaction between perchloric acid (HClO₄) and sodium hydroxide (NaOH) is:

HClO₄ (aq) + NaOH (aq) → NaClO₄ (aq) + H₂O (l)

Here's a breakdown:

* HClO₄ (aq) represents perchloric acid in an aqueous solution.

* NaOH (aq) represents sodium hydroxide in an aqueous solution.

* NaClO₄ (aq) represents sodium perchlorate, the salt produced by the reaction, also in an aqueous solution.

* H₂O (l) represents water, the other product of the reaction, in its liquid state.

This reaction is a neutralization reaction, where an acid (HClO₄) and a base (NaOH) react to form a salt (NaClO₄) and water (H₂O).