\begin{tabular}{l} Simplify \\ \( \frac{36 m^{-4} n^{6}}{4 m n^{-2} p^{-4}} \) \\ \( \frac{9 n^{4} p^{4}}{m^{3}} \) \\ \( \frac{9 n^{8} p^{4}}{m^{5}} \) \\ \( \frac{9 m^{5}}{n^{8} p^{4}} \) \\ \( \frac{9 n^{8}}{m m^{5} p^{4}} \) \\ \hline\end{tabular}
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Let's simplify each expression step by step. 1. **First Expression:** \[ \frac{36 m^{-4} n^{6}}{4 m n^{-2} p^{-4}} = \frac{36}{4} \cdot \frac{n^{6}}{n^{-2}} \cdot \frac{p^{4}}{m^{-4} m} = 9 \cdot n^{6 + 2} \cdot p^{4} \cdot m^{-4 - 1} = 9 n^{8} p^{4} m^{-5} \] 2. **Second Expression:** \[ \frac{9 n^{4} p^{4}}{m^{3}} \] 3. **Third Expression:** \[ \frac{9 n^{8} p^{4}}{m^{5}} \] 4. **Fourth Expression:** \[ \frac{9 m^{5}}{n^{8} p^{4}} \] 5. **Fifth Expression:** \[ \frac{9 n^{8}}{m m^{5} p^{4}} = \frac{9 n^{8}}{m^{6} p^{4}} \] Now, let’s summarize the simplified expressions: 1. First Expression Simplified: \( 9 n^{8} p^{4} m^{-5} \) 2. Second Expression: \( \frac{9 n^{4} p^{4}}{m^{3}} \) 3. Third Expression: \( \frac{9 n^{8} p^{4}}{m^{5}} \) 4. Fourth Expression: \( \frac{9 m^{5}}{n^{8} p^{4}} \) 5. Fifth Expression: \( \frac{9 n^{8}}{m^{6} p^{4}} \) These are the simplified forms of the given expressions! If you need any further analysis or explanations, let me know!
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