1. **State the problem:** Simplify the expression $$(64n^3)^{\frac{1}{3}}$$. 2. **Recall the rule:** When raising a power to a fractional exponent, use the rule $$a^{\frac{m}{n}} = \sqrt[n]{a^m}$$. Here, the exponent $$\frac{1}{3}$$ means the cube root. 3. **Apply the cube root:** $$ (64n^3)^{\frac{1}{3}} = \sqrt[3]{64n^3} $$. 4. **Separate the cube root:** $$ \sqrt[3]{64n^3} = \sqrt[3]{64} \times \sqrt[3]{n^3} $$. 5. **Evaluate each cube root:** - $$ \sqrt[3]{64} = 4 $$ because $$4^3 = 64$$. - $$ \sqrt[3]{n^3} = n $$ because the cube root and cube cancel out. 6. **Combine the results:** $$4 \times n = 4n$$. **Final answer:** $$\boxed{4n}$$