1. **State the problem:** Simplify the expression $(64n^6)^{\frac{1}{3}}$. 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:** $(64n^6)^{\frac{1}{3}} = \sqrt[3]{64n^6}$. 4. **Separate the cube root:** $\sqrt[3]{64n^6} = \sqrt[3]{64} \times \sqrt[3]{n^6}$. 5. **Evaluate each cube root:** - $\sqrt[3]{64} = 4$ because $4^3 = 64$. - $\sqrt[3]{n^6} = n^{\cancel{6} \div 3} = n^2$ because $\sqrt[3]{n^6} = n^{6 \times \frac{1}{3}} = n^2$. 6. **Combine the results:** $4 \times n^2 = 4n^2$. **Final answer:** $\boxed{4n^2}$