ANSWER
Option D
[tex]\sqrt[3]{40x^{23}}[/tex]
EXPLANATION
Given:
[tex]\frac{\sqrt[3]{200x^{24}}}{\sqrt[3]{5x}}[/tex]
Applying the law of surds and indices
[tex]\frac{\sqrt{M}}{\sqrt{N}}\text{ = }\sqrt{\frac{M}{N}}[/tex]
i.e:
[tex]\begin{gathered} \frac{\sqrt[3]{200x^{24}}}{\sqrt[3]{5x}} \\ \text{ = }\sqrt[3]{\frac{200x^{24}}{5x}} \\ \text{ = }\sqrt[3]{40x^{23}} \end{gathered}[/tex]
Hence, the correct answer is option D.
