1. **Problem Statement:** Simplify the expression $$(3x^2)^3$$. 2. **Step 1: Apply the power to both the coefficient and the variable inside the parentheses.** $$(3x^2)^3 = 3^3 \times (x^2)^3$$ 3. **Step 2: Calculate the powers separately.** $3^3 = 27$ 4. **Step 3: Use the exponent multiplication rule for $x$.** $$(x^2)^3 = x^{2 \times 3} = x^6$$ 5. **Step 4: Combine the results.** $$27x^6$$ **Final Answer:** $$(3x^2)^3 = 27x^6$$