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Properties of Exponents

Eighth graders learn the exponent rules — add exponents to multiply, subtract to divide, and know that any nonzero number to the zero power is 1 — the shortcuts that make working with powers fast and accurate.

Grade 8Exponents50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
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Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Use the product rule.
  • ✓Use the quotient rule.
  • ✓Use the power rule.
  • ✓Understand the zero exponent.
Essential Question

x³ · x⁴ — do you multiply the exponents, or add them? The rules of exponents turn messy multiplication into simple shortcuts. What are they?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Model · Interactive Tool

Apply the Rules

Project each item and have students simplify using the exponent rules. The tool explains each property.

🔤 Simplify using the exponent rulesTry it
Simplify each expression using the exponent rules.
The Lesson · Gradual Release (I Do · We Do · You Do)

50 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — Add or Multiply?

5 min

x³ · x⁴ — do you add or multiply the exponents?

👩‍🏫 Teacher Moves

  • Show x³ · x⁴.
  • Ask what happens to the exponents.
  • Set the goal: exponent rules.

🎒 Student Actions

  • See the powers.
  • Guess the rule.
  • Predict it.
2

I Do — The Rules

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Product rule: add exponents.
  • Quotient rule: subtract.
  • Zero exponent = 1.

🎒 Student Actions

  • Learn product.
  • Learn quotient.
  • Learn zero rule.
3

We Do — Apply Together

13 min

Class uses Apply the Rules.

👩‍🏫 Teacher Moves

  • Simplify each expression.
  • Name the rule used.
  • Check by expanding.

🎒 Student Actions

  • Simplify each.
  • Name the rule.
  • Check it.
4

You Do — On Your Own

12 min

Students simplify.

👩‍🏫 Teacher Moves

  • Apply the exponent rules.
  • Combine rules.
  • Handle zero exponents.

🎒 Student Actions

  • Apply rules.
  • Combine them.
  • Use zero rule.
5

Close — Close

5 min

One expression.

👩‍🏫 Teacher Moves

  • Give an expression.
  • Simplify it.
  • Hand out the exit ticket.

🎒 Student Actions

  • Simplify it.
  • Name the rule.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics.

CCSS
8.EE.1

Know and apply the properties of integer exponents.

CCSS
8.EE.1

Generate equivalent numerical expressions with exponents.

CCSS
8.EE.4

Perform operations with numbers in scientific notation.

SMP
MP.7

Use structure in the exponent rules.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Exponent-rule reference card.
  • Sentence frame: “Multiply powers → ___ exponents.”
  • Expand to check.

Support & Access

IEP / 504
  • Start with the product rule.
  • Expand to see why.
  • Use a rules chart.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Use negative exponents.
  • Use the power of a power rule.
  • Simplify complex expressions.
Materials

What to gather

  • 📽️Projector / board
  • 🧮Calculators
  • 💻Apply the Rules
  • 📄Exponent-rule charts
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

exponenthow many times to multiply the basebasethe number being multipliedproduct ruleadd exponents when multiplyingquotient rulesubtract exponents when dividingpower rulemultiply exponents for a power of a powerzero exponentany nonzero base to the 0 is 1negative exponenta reciprocalsimplifyto write more simply
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
Simplify: y⁵ · y³.
y⁸ (add the exponents).
QUESTION 2
Simplify: a⁹ ÷ a⁴.
a⁵ (subtract the exponents).
QUESTION 3
What is 6⁰?
1.

Going deeper? Negative exponents.

Have students explore negative exponents — discovering that x⁻² = 1/x². A printable exponent-rules sheet is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Properties of ExponentsFlip
Card 1
Term
Tap to flip →
Meaning
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Nice work!

Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Properties of ExponentsQuiz
Score: 0
1 / 6
Question 1
0%

Nice work!

Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Properties of ExponentsPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: base, exponent, negative exponent, power rule, product rule, quotient rule, simplify, zero exponent
  1. the number being multiplied
  2. how many times to multiply the base
  3. add exponents when multiplying
  4. multiply exponents for a power of a power
  5. any nonzero base to the 0 is 1
  6. a reciprocal
  7. to write more simply
  8. subtract exponents when dividing

Part B · Show what you learned

  1. Simplify: y⁵ · y³.
  2. Simplify: a⁹ ÷ a⁴.
  3. What is 6⁰?
Answer key — Part A: 1) base · 2) exponent · 3) product rule · 4) power rule · 5) zero exponent · 6) negative exponent · 7) simplify · 8) quotient rule
Part B: 1) y⁸ (add the exponents). 2) a⁵ (subtract the exponents). 3) 1.