Step 1
Given
[tex]\frac{\sqrt[3]{d^{10}}}{\sqrt{d^5}}[/tex]
Required; To write as a single radical
Step 2
Write the expression as a single radical
[tex]\begin{gathered} \sqrt[3]{a}=a^{\frac{1}{3}} \\ \sqrt[3]{d^{10}}=d^{\frac{10}{3}} \\ \sqrt{d^5}=d^{\frac{5}{2}} \\ \frac{\sqrt[3]{d^{10}}}{\sqrt{d^5}}=\frac{d^{\frac{10}{3}}}{d^{\frac{5}{2}}}=d^{\frac{10}{3}-\frac{5}{2}}=d^{\frac{5}{6}} \\ \end{gathered}[/tex]
Answer; Therefore in the simplest radical form, the answer will be;
[tex]d^{\frac{5}{6}}=(\sqrt[6]{d})^5\text{ or }\sqrt[6]{d^5}[/tex]
