Lesson 60: Power 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 specifically on the Power Rule of Exponents, which explains how to simplify an exponent raised to another exponent.

Learning Objectives

• Apply the power rule correctly.
• Simplify expressions like (a^m)^n.
• Combine power rule with other exponent rules.

Topics Covered

• Power of a power rule
• Multiplying exponents
• Simplifying exponential expressions

Key Terms

• Power Rule: When raising a power to a power, multiply the exponents.
• Exponent: Indicates repeated multiplication.
• Base: The number being raised to a power.

Lesson Examples

Example 1

1. (4²)³
2. Multiply exponents: 2 × 3 = 6
3. Answer: 4⁶

Example 2

1. (5³)²
2. Multiply exponents: 3 × 2 = 6
3. Answer: 5⁶

Example 3 (Combined Rules)

1. (2²)³ × 2⁴
2. Power rule: 2⁶ × 2⁴
3. Product rule: 2¹⁰

Practice Problems

1. (3²)⁴
2. (7³)²
3. (2⁴)³
4. (5²)³ × 5

Tips & Common Mistakes

• Do NOT add exponents when using the power rule.
• Multiply the exponents.
• Apply other exponent rules after simplifying powers.

Summary

The power rule allows us to simplify expressions efficiently by multiplying exponents. Mastering this rule makes complex exponent problems manageable.

Challenge Problems

1. (6²)⁵
2. (3³)⁴ ÷ 3²
3. (2³)² × (2²)³