Question

Write problem as a single radical using the smallest possible root. 17

Answer 1

Step 1

Given

`\frac{\sqrt[3]{d^(10)}}{√(d^5)}`

Required; To write as a single radical

Step 2

Write the expression as a single radical

`\begin{gathered} \sqrt[3]{a}=a^{(1)/(3)} \\ \sqrt[3]{d^(10)}=d^{(10)/(3)} \\ √(d^5)=d^{(5)/(2)} \\ \frac{\sqrt[3]{d^(10)}}{√(d^5)}=\frac{d^{(10)/(3)}}{d^{(5)/(2)}}=d^{(10)/(3)-(5)/(2)}=d^{(5)/(6)} \\ \end{gathered}`

Answer; Therefore in the simplest radical form, the answer will be;

`d^{(5)/(6)}=(\sqrt[6]{d})^5\text{ or }\sqrt[6]{d^5}`