1. **State the problem:** Simplify the expression $$(x^3 y)^4$$ and express it in the form $$x^{?} y^{?}$$. 2. **Recall the exponent rule:** When raising a product to a power, apply the power to each factor inside the parentheses: $$ (ab)^n = a^n b^n $$ 3. **Apply the rule:** $$ (x^3 y)^4 = (x^3)^4 \cdot y^4 $$ 4. **Simplify each term:** Using the power of a power rule: $$ (x^3)^4 = x^{3 \times 4} = x^{12} $$ 5. **Write the final simplified expression:** $$ x^{12} y^4 $$ **Answer:** The simplified form is $$x^{12} y^4$$.