Lesson 59: Zero & Negative 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 explains the special cases of zero and negative exponents and how they relate to the quotient rule of exponents.

Learning Objectives

• Evaluate expressions with zero exponents.
• Rewrite negative exponents as reciprocals.
• Simplify expressions using zero and negative exponent rules.

Topics Covered

• Zero exponent rule
• Negative exponent rule
• Reciprocals

Key Terms

• Zero Exponent Rule: Any nonzero number raised to the 0 power equals 1.
• Negative Exponent: Indicates the reciprocal of the base raised to the positive exponent.
• Reciprocal: A number flipped over a fraction (e.g., 3 becomes 1/3).

Lesson Examples

Example 1: Zero Exponent

1. 7⁰
2. Any nonzero number to the zero power equals 1.
3. Answer: 1

Example 2: Negative Exponent

1. 4⁻²
2. Rewrite as reciprocal: 1 / 4²
3. 4² = 16
4. Answer: 1/16

Example 3: Simplifying

1. 5³ ÷ 5⁵
2. Subtract exponents: 3 − 5 = −2
3. Rewrite: 5⁻² = 1/5²
4. Answer: 1/25

Practice Problems

1. 9⁰
2. 2⁻³
3. 6⁴ ÷ 6⁶
4. (3⁻²)

Tips & Common Mistakes

• Zero exponent rule only works for nonzero bases.
• Negative exponents do NOT make numbers negative.
• Always rewrite final answers with positive exponents.

Summary

Zero exponents equal 1, and negative exponents create reciprocals. These rules extend the exponent system and prepare students for scientific notation and rational expressions.

Challenge Problems

1. 10⁻³
2. 8² ÷ 8⁵
3. (2³ × 2⁻⁵)