EngageNY
8th Grade Module 1
Topic A: Exponential Notation and Properties of Integer Exponents
In Topic A, students begin by learning the precise definition of exponential notation where the exponent is restricted to being a positive integer. In Lessons 2
and 3, students discern the structure of exponents by relating multiplication and division of expressions with the same base to combining like terms using the
distributive property and by relating multiplying three factors using the associative property to raising a power to a power.
Lesson 4 expands the definition of exponential notation to include what it means to raise a nonzero number to a zero power; students verify that the
properties of exponents developed in Lessons 2 and 3 remain true. Properties of exponents are extended again in Lesson 5 when a positive integer, raised to a
negative exponent, is defined. In Lesson 5, students accept the properties of exponents as true for all integer exponents and are shown the value of learning
them; in other words, if the three properties of exponents are known, then facts about dividing numbers in exponential notation with the same base and
raising fractions to a power are also known.
This Topic has 6 lessons.
Lesson 1: Exponential Notation
Problem Set
Materials
Lesson 1 Problem Set
Lesson 2:
Sample Solutions
Video Support
Video 1: Represent Repeated Multiplication: Stop at 3:48
Video 2: What Are Exponents? Stop at 3:56
Video 3: Exponential Notation: Stop at 1:13, start again at
1:37
Video 4: Apply Exponents to Negative Bases
Multiplication of Numbers in Exponential Form
Problem Set
Lesson 2 Problem Set
Materials
Sample Solutions
Video 1:
Video 2:
Video 3:
Video 4:
patterns
Multiplying Exponential Expressions
Multiply Two Or More Exponential Expressions
Divide Exponential Expressions Part I
Divide Exponential Expressions by noticing
Lesson 3: Numbers in Exponential Form Raised to a Power
Problem Set
Lesson 3 Problem Set
Materials
Sample Solutions
Video 1: Raising Exponential Expressions to Powers
Video 2: Raise an Exponential Expression to a Power
Lesson 4: Numbers Raised to the Zeroth Power
Problem Set
Materials
Lesson 4 Problem Set
Lesson 5: Negative Exponents and Laws of Exponents
Lesson 5 Problem Set
Lesson 6: Proofs of Laws of Exponents
Lesson 6 Problem Set
Sample Solutions
Video 1: Apply a Zero Exponent Using Patterns & Rules
Video 2: Simplify Expressions and 0 and Negative
Exponents: End at 2:00
Video 1: Apply a Negative Exponent
Video 2: Simplify Expressions With Negative Exponents
Video 3: Expressions With 0 and Negative Exponents: Start
at 2:00
Video 4: Expressions With 0 and Negative Exponents
Video 5: Exponents Rules: End at 5:00
Video 1: Exponents Rules Part 2: Watch from 4:05-7:28
Video 2: What's the Power of a Power Rule?
Video 3: What's the Quotient of Powers Rule?