Author note — to cover

Applying one index across a product and across a quotient: (2 x 5) cubed and (3/4) squared, numeric bases only; combining with earlier laws in one simplification. Teach before negative-index-of-a-fraction, which uses the quotient case. Algebraic brackets like (2x cubed) squared live in Algebra. Both tiers. (N7)

• Fluency — direct questions on powers of a product and a quotient, 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).