Concept:
The oxidation of alkyl side chains on an aromatic ring using strong oxidizing agents like alkaline $KMnO_4$ is a standard method to produce carboxylic acids. Regardless of the length of the alkyl chain, it is oxidized down to a single $-COOH$ group, provided there is at least one benzylic hydrogen present.
Step 1: Analyze the starting material.
The reactant is an alkylbenzene (specifically, isobutylbenzene). The carbon atom directly attached to the benzene ring (the benzylic carbon) is attached to one hydrogen atom.
Step 2: Apply the oxidation rule.
When treated with hot alkaline $KMnO_4$, any alkyl group with at least one benzylic hydrogen is oxidized completely to a carboxyl group.
• The entire isobutyl side chain is cleaved.
• The benzylic carbon is converted to a carboxylate group ($-COOK$ in the presence of $KOH$).
Step 3: Identify the final product.
The aromatic ring remains intact, and the side chain becomes a $-COOK$ group. The resulting product is potassium benzoate.