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Is there a nice formula or expanded out formula for the generic sum \begin{align*} \left( \sum_{i = 1}^n |A_i| \right)^p? \end{align*} I was unsure what to search for. Expanded out, this leads to a sum of $n\cdot p$ terms with a lot of mixed-up stuff powers and stuff. Perhaps one could just apply the distributive law repeatedly to end up with a formula?

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