Simplify the following: $\frac{8^{\frac{1}{2}}}{8^{\frac{2}{3}}}$

Let $a=8,m=\frac{1}{2}$ and $n=\frac{2}{3}$.
Now we use $\frac{a^m}{a^n}=a^{m-n}$
$$\begin{gathered} \frac{8^{\frac{1}{2}}}{8^{\frac{2}{3}}}=8^{\frac{1}{2}-\frac{2}{3}} \\ =8^{\frac{3-4}{6}} \\ =8^{-\frac{1}{6}} \end{gathered}$$

Hence, after simplification, we get $\frac{8^{\frac{1}{2}}}{8^{\frac{2}{3}}}=8^{-\frac{1}{6}}$.