Essay

Training Guide: Explaining Exponential Expansion

You are a lead billing assistant at a utility billing firm. A new clerk is reviewing some energy adjustment formulas in the billing manual and encounters the general algebraic term ama^m and a specific adjustment factor written as (9)5(-9)^5. They are unsure what the term 'expand' means in this context and how to write these expressions in expanded form.

To help the new clerk, write a short explanation (an essay) that addresses the following:

  1. Define what it means to 'expand' an exponential expression.
  2. Recall and write the general algebraic expansion for the expression ama^m, explaining what the base is and how many times it is used as a factor.
  3. Recall and write the specific expanded notation for the term (9)5(-9)^5, clearly identifying its base and exponent, and stating how many times the base is multiplied by itself.
  4. Explain why keeping the parentheses around the base 9-9 is crucial when writing out the expanded multiplication.

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Updated 2026-06-17

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