1. **State the problem:** Calculate $12^3 \times 12^2$. 2. **Formula used:** When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$ 3. **Apply the rule:** Here, the base is 12, so: $$12^3 \times 12^2 = 12^{3+2} = 12^5$$ 4. **Calculate the value:** $$12^5 = 12 \times 12 \times 12 \times 12 \times 12 = 248832$$ 5. **Final answer:** $$12^3 \times 12^2 = 248832$$