Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Foundations Of Functions And Composition
Introduction: Extending the Pattern
Exponents follow consistent patterns. When we multiply powers, we add exponents. When we divide powers, we subtract exponents. These patterns hold even when the exponents are zero or negative. Understanding zero and negative exponents extends our ability to work with powers in algebra.
The Zero Exponent Rule
Any non-zero base raised to the zero power equals 1.
b⁰ = 1, where b ≠ 0
Why Does This Make Sense?
Consider the pattern when decreasing exponents:
2³ = 8 2² = 4 2¹ = 2 2⁰ = ?
Each time the exponent decreases by 1, the value is divided by 2. Continuing the pattern:
2⁰ = 2¹ ÷ 2 = 2 ÷ 2 = 1
This pattern holds for any non-zero base.
Examples
| Expression | Simplified | | 5⁰ | 1 | | (1,000)⁰ | 1 | | x⁰ (x ≠ 0) | 1 | | (3y)⁰ | 1 |