Slide Deck
Power Play: Integer Exponents
8th Grade • Tier 1 • 30 Minutes
Explore, simplify, and master exponent rules!
Welcome students and introduce the lesson title. Hook: Emphasize how exponent rules help simplify huge numbers and power your math skills.
Learning Targets & Success Criteria
Learning Targets:
• I can apply the product, quotient, and power rules of exponents to generate equivalent expressions.
• I can simplify expressions with integer exponents accurately.
Success Criteria:
• I simplify expressions using exponent rules without errors.
• I justify each step when generating equivalent expressions.
Clearly read out the Learning Targets and Success Criteria. Ask students to restate in their own words.
Warm‐Up Practice
Simplify each on your whiteboard:
- x² · x³
- (y⁵) ÷ (y²)
- (a²)³
Distribute mini whiteboards. Display each expression one at a time. Students write and hold up responses. Reference the Exponent Properties Reference Sheet if needed.
Key Exponent Rules
Product Rule:
• aᵐ · aⁿ = aᵐ⁺ⁿ
Quotient Rule:
• aᵐ ÷ aⁿ = aᵐ⁻ⁿ
Power Rule:
• (aᵐ)ⁿ = aᵐ·ⁿ
Present each rule and provide a quick verbal example. Point students to the reference sheet for support.
Worked Examples
- x² · x³ = x²⁺³ = x⁵
- (y⁵) ÷ (y²) = y⁵⁻² = y³
- (a²)³ = a²·³ = a⁶
Work through each example step‐by‐step, asking students to identify which rule applies.
Guided Practice
In pairs, complete Problems 1–6 on the Power Play Practice Worksheet.
• Cite which rule you used.
• Explain your reasoning to your partner.
Pair students and distribute the Power Play Practice Worksheet. Circulate and ask guiding questions.
Independent Check & Exit Ticket
Individually, complete 3 problems in the Simplify Exponents Interactive Quiz.
• Select the correct exponent rule for each.
• Submit your responses to record your understanding.
Explain that this is the individual exit ticket. Monitor student responses and collect analytics for future planning.
Worksheet
Power Play Practice Worksheet
Complete the following problems. For each:
- Simplify the expression fully.
- State which exponent rule you used.
- Justify your step(s).
1. Simplify: (x^4 \cdot x^{-2})
Answer:
Rule Used: ____________________________
Justification:
2. Simplify: ((3a^2b^3) \cdot (2a^3b^{-1}))
Answer:
Rule Used: ____________________________
Justification:
3. Simplify: (\frac{5x^6}{x^2})
Answer:
Rule Used: ____________________________
Justification:
4. Simplify: ((m^3n^2)^4)
Answer:
Rule Used: ____________________________
Justification:
5. Simplify: (2x^0y^5)
Answer:
Rule Used: ____________________________
Justification:
6. Simplify: (\frac{a^5b^{-2}}{a^{-2}b^3})
Answer:
Rule Used: ____________________________
Justification:
Reading
Exponent Properties Reference Sheet
This reference sheet summarizes the key rules for working with integer exponents. Keep it handy as you simplify expressions and generate equivalent forms.
1. Terminology
• Base (a): The factor being multiplied.
• Exponent (n or m): The number of times the base is used as a factor.
Notation: aⁿ means “multiply a by itself n times.”
Example: 2³ = 2 · 2 · 2 = 8
2. Product Rule
When you multiply two expressions with the same base, keep the base and add the exponents.
Formula: aᵐ · aⁿ = aᵐ⁺ⁿ
Example: x² · x³ = x²⁺³ = x⁵
3. Quotient Rule
When you divide two expressions with the same base, keep the base and subtract the exponent in the denominator from the exponent in the numerator.
Formula: aᵐ ÷ aⁿ = aᵐ⁻ⁿ (a ≠ 0)
Example: y⁵ ÷ y² = y⁵⁻² = y³
4. Power Rule
When you raise an exponential expression to another exponent, multiply the exponents.
Formula: (aᵐ)ⁿ = aᵐ·ⁿ
Example: (a²)³ = a²·³ = a⁶
5. Power of a Product
When a product is raised to a power, apply the exponent to each factor.
Formula: (ab)ⁿ = aⁿbⁿ
Example: (3x)² = 3² · x² = 9x²
6. Power of a Quotient
When a quotient is raised to a power, apply the exponent to both numerator and denominator.
Formula: (a/b)ⁿ = aⁿ/bⁿ (b ≠ 0)
Example: (x/2)³ = x³/2³ = x³/8
7. Zero Exponent Rule
Any nonzero base raised to the zero power equals 1.
Formula: a⁰ = 1 (a ≠ 0)
Example: 5⁰ = 1
8. Negative Exponent Rule
A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent.
Formula: a⁻ⁿ = 1/aⁿ (a ≠ 0)
Example: 2⁻³ = 1/2³ = 1/8
Keep this sheet visible during practice. Refer to the specific rule you’re using each time you simplify an expression!
Quiz
Simplify Exponents Interactive Quiz
Lesson Plan
Power Play Lesson Plan
Students will apply the product, quotient, and power rules of integer exponents to generate and simplify equivalent expressions, demonstrating mastery through guided and independent practice.
Mastering exponent rules builds fluency in scientific notation, factoring, and algebraic manipulation—key skills for success in high school math and beyond.
Audience
8th Grade
Time
30 minutes
Approach
Direct instruction followed by scaffolded practice.
Materials
- Exponent Properties Reference Sheet, - Power Play Practice Worksheet, - Simplify Exponents Interactive Quiz, and - Whiteboard and Markers
Prep
Prepare Materials
10 minutes
- Print copies of Exponent Properties Reference Sheet and Power Play Practice Worksheet
- Set up Simplify Exponents Interactive Quiz on classroom devices or LMS
- Review the product, quotient, and power rules of exponents and the success criteria
Step 1
Learning Targets & Success Criteria
3 minutes
- Display and read aloud the learning targets and success criteria:
- Learning Targets:
- I can apply the product rule, quotient rule, and power rule of exponents to generate equivalent expressions.
- I can simplify expressions with integer exponents accurately.
- Success Criteria:
- I can correctly simplify expressions using exponent rules without errors.
- I can justify each step when generating equivalent expressions.
- Learning Targets:
- Clarify any questions and have students rephrase targets in their own words.
Step 2
Warm-Up Practice
5 minutes
- Give each student a mini whiteboard and marker.
- Present three simple expressions (e.g., x²·x³, (y⁵)/(y²), (a²)³).
- Students simplify on whiteboards, then hold up answers.
- Use the Exponent Properties Reference Sheet for on-the-spot support.
- Quickly address common misconceptions.
Step 3
Direct Instruction
7 minutes
- Introduce the three key exponent rules using a visual organizer:
- Product Rule: aᵐ · aⁿ = aᵐ⁺ⁿ
- Quotient Rule: aᵐ ÷ aⁿ = aᵐ⁻ⁿ
- Power Rule: (aᵐ)ⁿ = aᵐ·ⁿ
- Model simplifying two worked examples step-by-step on the whiteboard.
- Highlight how each step aligns with the Exponent Properties Reference Sheet.
Step 4
Guided Practice
10 minutes
- Students pair up and work through Problems 1–6 on the Power Play Practice Worksheet.
- Circulate to monitor understanding and prompt students to cite which rule they’re using.
- Use guiding questions:
- “Which rule applies here?”
- “How did you combine the exponents?”
- Encourage partners to explain their reasoning to each other.
Step 5
Independent Check & Exit Ticket
5 minutes
- Students complete 3 expressions in the Simplify Exponents Interactive Quiz individually.
- Ensure they select the correct rule for each problem.
- Collect quick analytics from the quiz to gauge readiness:
- Identify any persistent errors for tomorrow’s lesson planning.