Lesson 57: Introduction to Exponents

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• Lesson Description
• Learning Objectives
• Topics Covered
• Key Terms
• Lesson Examples
• Practice Problems
• Tips & Common Mistakes
• Summary
• Challenge Problems
• Unit Navigation

Lesson Description

This lesson introduces exponents as a shorthand method for repeated multiplication. Students will learn the meaning of base and exponent, how to evaluate expressions, and how exponential notation simplifies large repeated products.

Learning Objectives

• Identify the base and exponent in exponential expressions.
• Rewrite repeated multiplication using exponent notation.
• Evaluate simple exponential expressions.

Topics Covered

• Repeated multiplication
• Base and exponent
• Evaluating powers

Key Terms

• Exponent: The number that tells how many times the base is multiplied by itself.
• Base: The number being multiplied repeatedly.
• Power: The result of raising a base to an exponent.

Lesson Examples

Example 1: Writing Repeated Multiplication

1. 5 × 5 × 5 × 5
2. This is 5 multiplied by itself 4 times.
3. Write as 5⁴.

Example 2: Evaluating an Exponent

1. 3³ means 3 × 3 × 3.
2. Multiply step by step: 3 × 3 = 9.
3. 9 × 3 = 27.

Practice Problems

1. Rewrite 2 × 2 × 2 × 2 × 2 using exponent notation.
2. Evaluate 4².
3. Evaluate 6³.
4. Write 7 × 7 using exponent form.

Tips & Common Mistakes

• The exponent tells how many times to multiply, not what to multiply by.
• Do not multiply base and exponent together.
• Always multiply step-by-step to avoid arithmetic errors.

Summary

Exponents provide a compact way to represent repeated multiplication. Understanding base and exponent is essential before learning exponent rules and advanced applications.

Challenge Problems

1. Evaluate 2⁵.
2. Write 9 × 9 × 9 × 9 × 9 × 9 in exponent form.
3. If a square has side length 4 units, what is its area written using exponents?