Power Up Your Knowledge: Exploring Exponents with Negative Bases

PreAlgebra Grades High School 9:02 Video
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Lesson Description

Learn how to evaluate exponents with negative bases. Understand the importance of parentheses and how they affect the outcome. This lesson will guide you through examples and provide practice problems to master this concept.

Video Resource

Exponents with Negative Bases | Math with Mr. J

Math with Mr. J

Duration: 9:02
Watch on YouTube

Key Concepts

  • Exponents indicate repeated multiplication of the base.
  • Parentheses determine whether a negative sign is part of the base.
  • The order of operations (PEMDAS/BODMAS) is crucial for correct evaluation.

Learning Objectives

  • Students will be able to evaluate exponents with negative bases when the negative sign is inside parentheses.
  • Students will be able to evaluate exponents with negative bases when the negative sign is outside parentheses.
  • Students will be able to explain the difference in the process and the results when parentheses are present versus absent.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the basic definition of an exponent and its components (base and power). Briefly discuss the order of operations.
  • Video Presentation (10 mins)
    Play the "Exponents with Negative Bases | Math with Mr. J" video. Encourage students to take notes on the examples provided.
  • Guided Practice (15 mins)
    Work through additional examples with the class, emphasizing the role of parentheses. Start with simple examples and gradually increase the complexity. Have students explain their reasoning at each step.
  • Independent Practice (15 mins)
    Provide students with a worksheet containing similar problems. Circulate the classroom to offer assistance and answer questions.
  • Review and Wrap-up (5 mins)
    Review the main concepts and address any remaining questions. Preview the next lesson on a related topic (e.g., negative exponents).

Interactive Exercises

  • Think-Pair-Share
    Present a problem on the board (e.g., (-4)^3). Have students individually solve the problem. Then, they pair up with a classmate to compare answers and discuss their solution methods. Finally, have a few pairs share their solutions with the class.
  • Error Analysis
    Provide a problem with an incorrect solution. Have students identify the mistake and explain how to correct it.

Discussion Questions

  • How does the presence or absence of parentheses affect the value of an expression with a negative base and an exponent?
  • Can you provide an example where the presence of parentheses does not change the outcome?
  • Explain in your own words how to evaluate (-3)^2 versus -3^2.

Skills Developed

  • Applying the order of operations
  • Understanding and applying the properties of exponents
  • Problem-solving and critical thinking
  • Attention to detail
  • Distinguishing between similar mathematical expressions

Multiple Choice Questions

Question 1:

What does an exponent tell you to do?

Correct Answer: Multiply the base by itself a certain number of times

Question 2:

What is the value of (-2)^4?

Correct Answer: 16

Question 3:

What is the value of -2^4?

Correct Answer: -16

Question 4:

Which expression is equivalent to (-5)^3?

Correct Answer: -5 * -5 * -5

Question 5:

Which expression is equivalent to -4^2?

Correct Answer: -(4 * 4)

Question 6:

What is the value of (-1)^5?

Correct Answer: -1

Question 7:

What is the value of -1^5?

Correct Answer: -1

Question 8:

What is the first step in evaluating -3^2?

Correct Answer: Multiply 3 by 3 and then apply the negative sign

Question 9:

Why are parentheses important when dealing with exponents and negative bases?

Correct Answer: Parentheses indicate that the negative sign is part of the base

Question 10:

What is the value of (-6)^2?

Correct Answer: 36

Fill in the Blank Questions

Question 1:

An exponent tells us how many times to multiply the ______ by itself.

Correct Answer: base

Question 2:

In the expression (-7)^2, the negative sign is ______ the base.

Correct Answer: part of

Question 3:

In the expression -5^2, the negative sign is ______ the base.

Correct Answer: not part of

Question 4:

(-3)^4 equals ______.

Correct Answer: 81

Question 5:

-3^4 equals ______.

Correct Answer: -81

Question 6:

When a negative number is raised to an even power (and is within parentheses) the answer is always ______.

Correct Answer: positive

Question 7:

When a negative number is raised to an odd power (and is within parentheses) the answer is always ______.

Correct Answer: negative

Question 8:

The order of operations tells us to evaluate exponents ______ multiplication or addition.

Correct Answer: before

Question 9:

The expression -1^6 equals ______.

Correct Answer: -1

Question 10:

The expression (-1)^6 equals ______.

Correct Answer: 1

Educational Standards

PA.N.1.1:Develop and apply the properties of integer exponents, including a^0 = 1 (with a ≠ 0), to generate equivalent numerical and algebraic expressions. PA.A.3.2:Justify steps in generating equivalent expressions by combining like terms and using order of operations (to include grouping symbols). Identify the properties used, including the properties of operations (associative, commutative, and distributive).

Teaching Materials

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