Author note — to cover

Subtracting indices when dividing powers of the same numeric base, derived by cancelling repeated factors; keep results at positive indices here, handing subtractions that give zero or negative answers to zero-index and negative-indices. Algebraic bases live in Algebra. Both tiers. (N7)

• Fluency — direct questions on dividing powers of the same base, limited to this lesson's stated scope (4 questions).
• Application — use the same skill in unfamiliar or contextual questions without introducing a later method (4 questions).
• Check — questions built around the exclusions and likely misconceptions named in the lesson brief (4 questions).