Simplify. Express your answer using positive exponents. \( \frac{8 p q^{8} r^{8}}{2 p q^{2} r^{5}} \) \begin{tabular}{|l|l|}\hline\( \square \) & \( \frac{\square}{\square} \) \\ \hline\end{tabular}

To simplify the expression \( \frac{8 p q^{8} r^{8}}{2 p q^{2} r^{5}} \), you start by dividing the coefficients and then apply the laws of exponents to the variables. 1. **Coefficients**: \( \frac{8}{2} = 4 \) 2. **For \( p \)**: \( \frac{p}{p} = 1 \) (It cancels out) 3. **For \( q \)**: \( q^{8} / q^{2} = q^{8-2} = q^{6} \) 4. **For \( r \)**: \( r^{8} / r^{5} = r^{8-5} = r^{3} \) Putting it all together, you get: \[ \frac{8 p q^{8} r^{8}}{2 p q^{2} r^{5}} = 4 q^{6} r^{3} \] Thus, the simplified expression is \( 4 q^{6} r^{3} \). \begin{tabular}{|l|l|}\hline 4 & \( \frac{q^{6} r^{3}}{1} \) \\ \hline\end{tabular}