Lesson 61: Quotient Rule 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 focuses on the Quotient Rule of Exponents, which allows us to simplify expressions when dividing powers that share the same base.

Learning Objectives

• Apply the quotient rule correctly.
• Simplify division expressions with exponents.
• Understand how the quotient rule connects to negative exponents.

Topics Covered

• Dividing powers with the same base
• Subtracting exponents
• Connections to negative exponents

Key Terms

• Quotient Rule: When dividing powers with the same base, subtract the exponents.
• Base: The repeated factor in an exponential expression.
• Exponent: The number that indicates repeated multiplication.

Lesson Examples

Example 1

1. 8⁶ ÷ 8²
2. Subtract exponents: 6 − 2 = 4
3. Answer: 8⁴

Example 2

1. 5⁹ ÷ 5⁴
2. Subtract exponents: 9 − 4 = 5
3. Answer: 5⁵

Example 3 (Leading to Negative Exponents)

1. 3² ÷ 3⁵
2. Subtract exponents: 2 − 5 = −3
3. Rewrite: 3⁻³ = 1/3³

Practice Problems

1. 7⁸ ÷ 7³
2. 4⁵ ÷ 4⁷
3. 9³ ÷ 9
4. 2⁶ ÷ 2²

Tips & Common Mistakes

• Only subtract exponents when bases are the same.
• Do not divide the exponents.
• If the result is negative, rewrite using a reciprocal.

Summary

The quotient rule simplifies division problems involving exponents by subtracting exponents when the bases are identical. This rule connects directly to zero and negative exponents.

Challenge Problems

1. 10⁷ ÷ 10³
2. 6² ÷ 6⁵
3. (4⁴ ÷ 4²) × 4³