Simplify. Assume that all variables are positive. \( \begin{array}{ll}\text { c. } \sqrt[6]{64 x^{18}} & \text { d. } \sqrt[3]{\frac{x^{24}}{6}}\end{array} \)

To simplify \( \sqrt[6]{64 x^{18}} \), we first break it down. The number 64 can be expressed as \( 2^6 \), and \( x^{18} \) can be simplified under the sixth root as \( (x^3)^6 \). Therefore, we have: \[ \sqrt[6]{64 x^{18}} = \sqrt[6]{2^6} \cdot \sqrt[6]{(x^3)^6} = 2 \cdot x^3 = 2x^3. \] For \( \sqrt[3]{\frac{x^{24}}{6}} \), we can separate the components inside the root: \[ \sqrt[3]{\frac{x^{24}}{6}} = \frac{\sqrt[3]{x^{24}}}{\sqrt[3]{6}} = \frac{x^{8}}{\sqrt[3]{6}}. \] Thus, the simplified forms are: c: \( 2x^3 \) and d: \( \frac{x^{8}}{\sqrt[3]{6}} \).