Exponents and Exponential Functions

Lesson 5

Math

Unit 6

9th Grade

Lesson 5 of 22

Objective


Use negative exponent rules to analyze and rewrite exponential expressions.

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.
  • A.SSE.A.2 — Use the structure of an expression to identify ways to rewrite it. For example, see x4 — y4 as (x²)² — (y²)², thus recognizing it as a difference of squares that can be factored as (x² — y²)(x² + y²).

Foundational Standards

  • 6.EE.A.1

Criteria for Success


  1. Understand that $${x^{-m}={1\over x^m}}$$ and $${{1\over x^{-m}}=x^m}$$.
  2. Use properties of exponents to simplify expressions including negative and zero exponents. 
  3. Analyze the structure of an exponential expression and determine an efficient way to write a simplified equivalent expression (Standard for Mathematical Practice 7). 

Tips for Teachers


This lesson reviews skills and concepts from 8.EE.1. Depending on the needs of your students, this lesson may be skipped or used in a different way.

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Anchor Problems

25-30 minutes


Problem 1

Which expression is not equivalent to the given expression below?

$${{x^{-2}}\over{y^{-3}}}$$

a.   $${x^{-2}y^3}$$

b.   $${{y^3}\over{x^2}}$$

c.   $${1\over{x^2y^{-3}}}$$

d.   $${x^{-2}\cdot{1\over y^3}}$$

e.   $${y^3\cdot{1\over x^2}}$$

Guiding Questions

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Problem 2

Write the following expression without negative exponents.

$${(2x^{-2}3y^2)^{-1}\over{x^5y^{-2}}}$$

Guiding Questions

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Problem Set

15-20 minutes


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

Target Task

5-10 minutes


Given that $${x>1}$$ and $$s$$ represents the value of the expression, put a check mark in the appropriate column to indicate the value, $$s$$, of each expression.

  $$0<s<1$$ $$-1<s<0$$ $$s\geq1$$ or $$s\leq-1$$
$${x^{-3}}$$      
$$-{x^{-3}}$$      
$${1\over{(-2x)^2}}$$      
$${\left({1\over x}\right)^{-4}}$$      

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.

  • Include error analysis problems

Next

Define rational exponents and convert between rational exponents and roots.

Lesson 6
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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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