Power Up: Exponent Essentials!

Katherine Turner

Tier 1

Lesson Plan

Power Up: Exponent Essentials!

Students will be able to define exponents and apply the basic rules of multiplication, division, and power of a power to simplify expressions.

Understanding exponents is fundamental for success in algebra and beyond. This lesson helps students build a strong foundation for future mathematical topics and practical applications.

Audience

9th Grade

Time

30 minutes

Approach

Interactive lecture, guided practice, and independent application.

Materials

Whiteboard or Projector, Power Up: Exponent Essentials! Slide Deck, Exponent Warm-Up, Exponent Practice Worksheet, and Exponent Practice Answer Key

Prep

Teacher Preparation

15 minutes

Review the Power Up: Exponent Essentials! Slide Deck and lesson content.
- Print copies of the Exponent Warm-Up (one per student).
- Print copies of the Exponent Practice Worksheet (one per student).
- Have the Exponent Practice Answer Key ready for reference.
- Ensure projector/whiteboard is set up for the slide deck.

Step 1

Warm-Up: What's the Power?

5 minutes

Distribute the Exponent Warm-Up.
* Instruct students to complete the warm-up individually. This activates prior knowledge about repeated multiplication.
* Briefly review answers as a class, addressing any initial misconceptions.

Step 2

Introduction to Exponents

8 minutes

Use the Power Up: Exponent Essentials! Slide Deck to introduce the concept of exponents: base, exponent, and power.
* Explain why exponents are useful (shorthand for repeated multiplication, real-world examples).
* Go through the first few slides explaining the definition and basic examples.

Step 3

Rules of Exponents: Guided Practice

10 minutes

Continue with the Power Up: Exponent Essentials! Slide Deck to introduce the rules for:
* Multiplying powers with the same base (add exponents).
* Dividing powers with the same base (subtract exponents).
* Power of a power (multiply exponents).
* Work through examples on the slide deck as a class, encouraging student participation.
* Pause for questions and clarify any confusing points.

Step 4

Independent Practice: Worksheet

5 minutes

Distribute the Exponent Practice Worksheet.
* Instruct students to begin working on the problems independently. Circulate to provide individual support and answer questions.
* If time permits, briefly review one or two problems using the Exponent Practice Answer Key.

Slide Deck

Welcome to Power Up: Exponent Essentials!

Today, we're diving into the world of exponents – a powerful tool in math!

What are exponents?

A shortcut for repeated multiplication.
They help us write very large or very small numbers easily.

Think about it: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 is a lot to write!

Welcome students and introduce the topic. Explain that exponents are a shorthand for repeated multiplication.

Anatomy of an Exponent

Let's break down what an exponent looks like:

Example: 2^3

Base: The number being multiplied (in this case, 2)
Exponent (or Power): The small number above the base that tells you how many times to multiply the base by itself (in this case, 3)
Power: The entire expression (2^3) and its value (8)

So, 2^3 means 2 x 2 x 2 = 8

Define the terms: base, exponent, and power. Use a clear example.

Rule 1: Product of Powers

When multiplying powers with the SAME base, ADD the exponents.

Formula: a^m * a^n = a^(m+n)

Example 1: 2^3 * 2^4 = 2^(3+4) = 2^7
(This is 2 x 2 x 2 multiplied by 2 x 2 x 2 x 2, which is seven 2s)

Example 2: x^5 * x^2 = x^(5+2) = x^7

Introduce the first rule: Product of Powers. Emphasize that the bases must be the same.

Rule 2: Quotient of Powers

When dividing powers with the SAME base, SUBTRACT the exponents.

Formula: a^m / a^n = a^(m-n)

Example 1: 5^6 / 5^2 = 5^(6-2) = 5^4
(Imagine six 5s on top, two 5s on the bottom. Two 5s cancel, leaving four 5s on top)

Example 2: y^8 / y^3 = y^(8-3) = y^5

Introduce the second rule: Quotient of Powers. Again, highlight the same base requirement.

Rule 3: Power of a Power

When raising a power to another power, MULTIPLY the exponents.

Formula: (a^m)^n = a^(m*n)

Example 1: (3^2)^3 = 3^(2*3) = 3^6
(This means 3^2 multiplied by itself 3 times: (3x3) * (3x3) * (3x3) = six 3s)

Example 2: (z^4)^2 = z^(4*2) = z^8

Introduce the third rule: Power of a Power. Explain why we multiply the exponents.

Quick Review & Practice Time!

Let's quickly recap our rules:

Multiply (same base): ADD exponents
Divide (same base): SUBTRACT exponents
Power of a Power: MULTIPLY exponents

Now, let's put your new knowledge to the test with a practice worksheet!

Quick review and transition to the worksheet. Emphasize that practice is key.

Warm Up

Exponent Warm-Up: What's the Power?

Instructions: Take a few minutes to answer the following questions. Do your best to show any work!

What does 3 x 3 x 3 x 3 mean in a shorter mathematical way?
Calculate the value of 5 x 5.
If you have 4^2, what are the base and the exponent?
- Base:
- Exponent:
Is 2 + 2 + 2 the same as 2^3? Explain why or why not.

Worksheet

Exponent Practice Worksheet: Rule It!

Instructions: Simplify each expression using the rules of exponents. Show your work!

Part 1: Product of Powers (Multiplying with the Same Base)

2^3 * 2^5
x^4 * x^6
y * y^7

Part 2: Quotient of Powers (Dividing with the Same Base)

7^8 / 7^3
a^9 / a^2
m^10 / m^9

Part 3: Power of a Power

(4^3)^2
(b^5)^4
(w^2)^7

Part 4: Mixed Practice

(3^2 * 3^4) / 3^3
(p^7 / p^3)^2
(x^2)^3 * x^5

Answer Key

Exponent Practice Answer Key

Instructions: Review the solutions below and check your work.

Part 1: Product of Powers (Multiplying with the Same Base)

2^3 * 2^5
- Thought Process: When multiplying powers with the same base, add the exponents.
- Answer: 2^(3+5) = 2^8
x^4 * x^6
- Thought Process: When multiplying powers with the same base, add the exponents.
- Answer: x^(4+6) = x^10
y * y^7
- Thought Process: Remember that 'y' by itself has an implied exponent of 1 (y^1). Then, when multiplying powers with the same base, add the exponents.
- Answer: y^(1+7) = y^8

Part 2: Quotient of Powers (Dividing with the Same Base)

7^8 / 7^3
- Thought Process: When dividing powers with the same base, subtract the exponents.
- Answer: 7^(8-3) = 7^5
a^9 / a^2
- Thought Process: When dividing powers with the same base, subtract the exponents.
- Answer: a^(9-2) = a^7
m^10 / m^9
- Thought Process: When dividing powers with the same base, subtract the exponents.
- Answer: m^(10-9) = m^1 = m

Part 3: Power of a Power

(4^3)^2
- Thought Process: When raising a power to another power, multiply the exponents.
- Answer: 4^(3*2) = 4^6
(b^5)^4
- Thought Process: When raising a power to another power, multiply the exponents.
- Answer: b^(5*4) = b^20
(w^2)^7
- Thought Process: When raising a power to another power, multiply the exponents.
- Answer: w^(2*7) = w^14

Part 4: Mixed Practice

(3^2 * 3^4) / 3^3
- Thought Process: First, use the product of powers rule for the numerator, then the quotient of powers rule.
- Answer: (3^(2+4)) / 3^3 = 3^6 / 3^3 = 3^(6-3) = 3^3
(p^7 / p^3)^2
- Thought Process: First, use the quotient of powers rule inside the parentheses, then the power of a power rule.
- Answer: (p^(7-3))^2 = (p^4)^2 = p^(4*2) = p^8
(x^2)^3 * x^5
- Thought Process: First, use the power of a power rule for the first term, then the product of powers rule.
- Answer: x^(2*3) * x^5 = x^6 * x^5 = x^(6+5) = x^11