Overview
This lecture introduces powers (also called indices or orders), focusing on definitions, notation, and three basic exponent rules.
Introduction to Powers
- The power (index/order) is the small number written above and to the right of the base.
- The base is the number or variable being multiplied by itself.
- 3² means "3 to the power of 2" or "3 squared" (3 × 3 = 9).
- a³ means "a to the power of 3" or "a cubed" (a × a × a).
Key Exponent Rules
- Any base to the power of 0 equals 1 (e.g., 7⁰ = 1, p⁰ = 1, 36b⁰ = 1).
- Any base to the power of 1 equals itself (e.g., 7¹ = 7, p¹ = p, 36b¹ = 36b).
- Any base of 1 to any power equals 1 (e.g., 1⁵ = 1, 1^c = 1, 1^(12a) = 1).
Examples
- 3² = 9 because 3 × 3 = 9.
- a³ = a × a × a.
- e = e¹, so you can add a power of 1 without changing the value.
- 1^5 = 1 × 1 × 1 × 1 × 1 = 1.
Key Terms & Definitions
- Base — the number or variable being repeatedly multiplied.
- Power (Index/Order) — the small number indicating how many times the base is multiplied by itself.
- Squared — term for a base raised to the power of 2.
- Cubed — term for a base raised to the power of 3.
Action Items / Next Steps
- Memorize the three basic exponent rules.
- Practice writing and simplifying expressions using powers.