Exponents and Exponential Functions

Lesson 1

Math

Unit 6

9th Grade

Lesson 1 of 22

Objective


Use exponent rules to analyze and rewrite expressions with non-negative exponents.

Common Core Standards


Core Standards

  • 8.EE.A.1 — Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × 3-5 = 3-3 = 1/3³ = 1/27.

Foundational Standards

  • 6.EE.A.1

Criteria for Success


  1. Use the power, product, and quotient rules to simplify exponential expressions with non-negative exponents.
  2. Use the order of operations and properties of exponents to write equivalent expressions and to justify why two expressions are not equivalent.

Tips for Teachers


This lesson reviews skills and concepts from 8.EE.1 in order to set students up for success with the rest of the unit. Depending on the needs of your students, this lesson may be skipped or used in a different way. 

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Anchor Problems


Problem 1

Which expressions are equivalent to $${{(x^5x^4)^3}\over{x^2}}$$? Select all that apply.

a.   $${x^{25}}$$

b.   $${x^{30}}$$

c.   $${{x^{12}}\over{x^2}}$$

d.   $${{x^{27}}\over{x^2}}$$

e.   $${{x^{60}}\over{x^2}}$$

f.   $${{(x^9)^3}\over x^2}$$

g.   $${{(x^{20})^3}\over x^2}$$

Guiding Questions

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Problem 2

Simplify the following expression using the properties of exponents.

$${{{8a^4(7b)^3}\over 7ab^2} \times \left({7^2a}\over{8b^2}\right)^5}$$

Guiding Questions

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Problem 3

Is $${(x-y)^2}$$ equivalent to $${(x^2-y^2)}$$? Justify your answer.

Guiding Questions

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Problem Set


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task


Simplify the following expression using the properties of exponents.

$${{3x^3(y^2)^3}\over(2x^2)^3y^4}$$

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

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Lesson 2

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Exponent Rules, Expressions, and Radicals

Topic B: Arithmetic and Geometric Sequences

Topic C: Exponential Growth and Decay

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