1. **State the problem:** Simplify the expression $$(3x^6)^3 (2x^2)^4$$. 2. **Recall the exponent rules:** - Power of a power: $$(a^m)^n = a^{m \times n}$$ - Product of powers with the same base: $$a^m \times a^n = a^{m+n}$$ - Power of a product: $$(ab)^n = a^n b^n$$ 3. **Apply the power of a product rule:** $$(3x^6)^3 = 3^3 (x^6)^3 = 27 x^{18}$$ $$(2x^2)^4 = 2^4 (x^2)^4 = 16 x^{8}$$ 4. **Multiply the two results:** $$27 x^{18} \times 16 x^{8} = (27 \times 16) x^{18+8} = 432 x^{26}$$ 5. **Final answer:** $$\boxed{432 x^{26}}$$