Question

Simplify:$\sqrt{\frac{q^8}{q^{14}}\hspace{0.17em}}$

Short answer

The required answer is$\frac{1}{q^3}$.

Step-by-step solution

Step 1. Given information.  

The given square root is$\sqrt{\frac{q^8}{q^{14}}}$.

Step 2. Simplify the given root.  

$$\begin{gathered} \sqrt{\frac{q^8}{q^{14}}} \\ =\sqrt{\frac{1}{q^6}} \end{gathered}$$

Apply radical rule.

$$\begin{gathered} \frac{\sqrt{1}}{\sqrt{q^6}} \\ =\frac{1}{\sqrt{q^6}} \\ =\frac{1}{q^3} \end{gathered}$$