Question

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

Answer 1

Answer:

$\sqrt[6]{n^{23}}$

Explanation:

The given expression is

$\sqrt{n^5}\sqrt[3]{n^4}$

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

$n^{\frac{5}{2}}\cdot n^{\frac{4}{3}}$

Now, we can add the exponents

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

Finally, we can write the expression in radical form

$n^{\frac{23}{6}}=\sqrt[6]{n^{23}}$

Therefore, the answer is

$\sqrt[6]{n^{23}}$