1. The problem is to simplify the expression $a^2 b^2 c^2$. 2. Recall the rule of exponents: when multiplying powers with the same base, you add the exponents, but here each variable is raised to the power 2 separately. 3. The expression $a^2 b^2 c^2$ can be rewritten as $(abc)^2$ because $(abc)^2 = a^2 b^2 c^2$ by the property of exponents. 4. Therefore, the simplified form of $a^2 b^2 c^2$ is $$(abc)^2$$. 5. This means the product of $a$, $b$, and $c$ is squared. 6. Final answer: $a^2 b^2 c^2 = (abc)^2$.