We will have the following:
[tex]\begin{gathered} \frac{\sqrt[3]{48x^{14}}}{\sqrt[3]{3x}}=\frac{\sqrt[3]{8x^{12}\ast6x^2}}{\sqrt[3]{3x}}=\frac{2x^4\sqrt[3]{6x^2}}{\sqrt[3]{3x}} \\ \\ =2x^4\sqrt[3]{\frac{6x^2}{3x}}=2x^4\sqrt[3]{2x} \end{gathered}[/tex]
So, the simplification is:
[tex]2x^4\sqrt[3]{2x}[/tex]
