Exponent Extravaganza: Multiplying Powers with Different Bases

PreAlgebra Grades High School 2:24 Video
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Lesson Description

Learn how to multiply exponents when the bases are different but the powers are the same. This lesson breaks down the steps with clear examples and practice problems.

Video Resource

Multiplying Exponents with Different Bases and the Same Exponent | Math with Mr. J

Math with Mr. J

Duration: 2:24
Watch on YouTube

Key Concepts

  • Exponents
  • Bases
  • Multiplying exponents with the same exponent and different bases

Learning Objectives

  • Students will be able to identify the base and exponent in a given expression.
  • Students will be able to multiply exponential expressions with different bases and the same exponent.
  • Students will be able to simplify expressions resulting from the multiplication of exponents.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the basic concept of exponents (base and power). Briefly discuss what happens when multiplying exponents with the *same* base (add the exponents) as a warm-up, referencing the linked video in the description if needed. State that today's video lesson will focus on what to do when the bases are *different* and the exponents are the same.
  • Video Presentation (7 mins)
    Play the 'Multiplying Exponents with Different Bases and the Same Exponent | Math with Mr. J' video. Encourage students to take notes on the rule and the examples provided.
  • Guided Practice (10 mins)
    Work through the examples from the video on the board, explaining each step clearly. Emphasize the rule: (x^a) * (y^a) = (x*y)^a. Provide additional examples, such as (3^2) * (5^2), and guide students to solve them. Ensure they understand to multiply the bases and keep the exponent the same.
  • Independent Practice (10 mins)
    Provide students with a worksheet or online practice problems with varying levels of difficulty. Examples: (4^3) * (2^3), (7^4) * (3^4), (10^2) * (6^2).
  • Wrap-up & Assessment (8 mins)
    Review the key concept of multiplying exponents with different bases and the same exponent. Administer the multiple choice and fill-in-the-blank quizzes to assess student understanding.

Interactive Exercises

  • Exponent Matching Game
    Create a matching game where students have to match expressions like (2^3) * (4^3) with their simplified forms (8^3).

Discussion Questions

  • What is the difference between multiplying exponents with the same base versus different bases?
  • Why do we multiply the bases and keep the exponent the same when the bases are different and the exponents are the same?
  • Can you think of a real-world example where multiplying exponents with different bases might be useful?

Skills Developed

  • Applying exponent rules
  • Simplifying expressions
  • Problem-solving

Multiple Choice Questions

Question 1:

What is the rule for multiplying exponents with different bases and the same exponent?

Correct Answer: Multiply the bases and keep the exponent

Question 2:

Simplify: 2³ * 3³

Correct Answer: 6³

Question 3:

Which of the following is equivalent to (5²) * (4²)?

Correct Answer: 20²

Question 4:

What is the value of 10² * 2²?

Correct Answer: 20²

Question 5:

What is the first step in simplifying (6⁴) * (2⁴)?

Correct Answer: Multiply 6 and 2

Question 6:

Which expression is equal to 4⁵ * 1⁵?

Correct Answer: 4⁵

Question 7:

Simplify: 7² * 1²

Correct Answer: 7²

Question 8:

Solve for x: x = 3³ * 2³

Correct Answer: 6³

Question 9:

Which of these follows the rule for multiplying exponents?

Correct Answer: 2³ * 2³ = 2⁶

Question 10:

What is another way to write (8⁵) * (1⁵)?

Correct Answer: 8⁵

Fill in the Blank Questions

Question 1:

When multiplying exponents with different bases and the same exponent, you should ______ the bases.

Correct Answer: multiply

Question 2:

In the expression 5³ * 2³, the ______ are 5 and 2.

Correct Answer: bases

Question 3:

The simplified form of 4² * 3² is ______².

Correct Answer: 12

Question 4:

If a = 7 and b = 2, then a² * b² = (7*2)² = _______.

Correct Answer: 14²

Question 5:

To solve 9² * 1², we multiply 9 and 1 and keep the exponent of _______.

Correct Answer: 2

Question 6:

When multiplying exponents with the same power, the _______ stays the same.

Correct Answer: exponent

Question 7:

The answer to 12² * 1² is ________.

Correct Answer: 12²

Question 8:

The ______ is the number that is raised to a power.

Correct Answer: base

Question 9:

5³ * 4³ can be written as _______³.

Correct Answer: 20

Question 10:

If y² * z² = 81, and z = 3, then y = ______

Correct Answer: 3

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.3.1:Use substitution to simplify and evaluate algebraic expressions.

Teaching Materials

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