Lesson 58: Rules of 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 the fundamental rules of exponents that allow us to simplify expressions efficiently without writing out repeated multiplication.

Learning Objectives

• Apply the product rule of exponents.
• Apply the quotient rule of exponents.
• Apply the power of a power rule.

Topics Covered

• Product rule
• Quotient rule
• Power of a power

Key Terms

• Product Rule: Add exponents when multiplying same bases.
• Quotient Rule: Subtract exponents when dividing same bases.
• Power of a Power: Multiply exponents when raising a power to another power.

Lesson Examples

Example 1: Product Rule

1. 2³ × 2²
2. Add exponents: 3 + 2 = 5
3. Answer: 2⁵

Example 2: Quotient Rule

1. 5⁷ ÷ 5³
2. Subtract exponents: 7 − 3 = 4
3. Answer: 5⁴

Example 3: Power of a Power

1. (3²)³
2. Multiply exponents: 2 × 3 = 6
3. Answer: 3⁶

Practice Problems

1. 4² × 4³
2. 6⁵ ÷ 6²
3. (2³)²
4. 7⁴ × 7

Tips & Common Mistakes

• Rules only apply when bases are the same.
• Do not multiply exponents when multiplying expressions — add them.
• Be careful not to mix up subtraction and division.

Summary

The exponent rules simplify complex expressions efficiently. Mastery of these rules is essential before working with negative exponents and scientific notation.

Challenge Problems

1. (5²)⁴
2. 8⁶ ÷ 8²
3. 3³ × 3⁴ ÷ 3²