Properties of Exponents
I can use the exponent rules for products, powers and quotients, and explain each by counting factors.
What students learn
Students learn to multiply, divide and raise powers of one base by counting factors, with the coefficients worked as numbers.
See inside
The key rule
Keep the base and add the exponents when you multiply; if a rule slips your mind, write the factors out and count.
x² · x³ = x⁵; (x²)³ = x⁶
Simplest form: one number, each letter once. No variable on this sheet is 0.
Watch out
A student multiplies the exponents in x³ · x⁴.
The mistake: x³ · x⁴ = x¹²3 × 4 is the rule for (x³)⁴.
The fix: x³ · x⁴ = x⁷Three x's and four x's make seven x's.
The mistakes it targets
- Multiplies the exponents when powers of one base are multiplied
- Multiplies the bases as well as adding the exponents
- Leaves the coefficient out when raising a product to a power
- Drops the coefficient in a quotient
The interactive Teacher Deck (32 slides, PowerPoint)
- The Learn page taught on screen: 8 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (four steps), each with the reason for the step
- Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
- Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
- Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
- A completed deck PDF (19 pages) with every slide fully built, to print or post
The student packet (9 pages)
- Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
- Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
- Apply: one word problem, a reasoning prompt and one error analysis
- Assess: an exit ticket of four items, two per page, with an I-can self-rating
- Homework (page 5): eight new problems, two warm-up, four standard and two stretch
- Answer key (pages 6–7): every problem worked step by step, four common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
- Color and ink-saver editions of the whole packet
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.