Write equivalent expressions for \(x^ 7 \cdot x ^{-2}\) and \(\large \frac{x ^7}{x^ 2}\). What do you notice? Explain how your results relate to the properties of integer exponents.
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A toy store is creating a large window display of different colored cubes stacked in a triangle shape. The table shows the number of cubes in each row of the triangle, starting with the top row.
Evaluate \(– a^ n\) when a = 3 and n = 2, 3, 4, and 5. Now evaluate \((–a)^ n\) when a = 3 and n = 2, 3, 4, and 5. Based on this sample, does it appear that \(– a ^n = (–a) ^n\) ? If not, state the relationships, if any, between \(– a^ n \text{ and } ( –a)^ n \).
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