Question

11. Write ____ as a single radical using the smallest possible root.

Answer 1

`\sqrt[6]{n^(23)}`

Step-by-step explanation:

The given expression is

`√(n^5)\sqrt[3]{n^4}`

To simplify, we first need to write them in exponent form

`n^{(5)/(2)}\cdot n^{(4)/(3)}`

Now, we can add the exponents

`\begin{gathered} n^{(5)/(2)}\cdot n^{(4)/(3)}=n^{(5)/(2)+(4)/(3)}=n^{(23)/(6)} \\ \\ Because \\ (5)/(2)+(4)/(3)=(5(3)+2(4))/(2(3))=(15+8)/(6)=(23)/(6) \end{gathered}`

Finally, we can write the expression in radical form

`n^{(23)/(6)}=\sqrt[6]{n^(23)}`

Therefore, the answer is

`\sqrt[6]{n^(23)}`