Functions
AI Assistant

Exponent Rules

Master the 5 rules visually — see WHY they work on the graph

The exponent rules are patterns that emerge from repeated multiplication. Instead of memorizing formulas, this lesson lets you see each rule on the graph of y = 2ˣ.

The five rules: (1) aᵐ × aⁿ = aᵐ⁺ⁿ, (2) aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (3) (aᵐ)ⁿ = aᵐⁿ, (4) a⁰ = 1, and (5) a⁻ⁿ = 1/aⁿ.

Ask the AI anything — try "Why is anything to the 0 power equal to 1?" or "What does 2⁻³ mean?"

Graph

FAQ

Why is anything to the 0 power equal to 1?
Look at the pattern: 2³ = 8, 2² = 4, 2¹ = 2. Each step divides by 2. The next step: 2⁰ = 2 ÷ 2 = 1. The pattern forces it. Also, aⁿ ÷ aⁿ = a⁰ = 1 by the quotient rule.
What does a negative exponent mean?
A negative exponent means "take the reciprocal." 2⁻³ = 1/2³ = 1/8. On the graph, negative exponents give values between 0 and 1.
What are the 5 exponent rules?
(1) Product rule: aᵐ × aⁿ = aᵐ⁺ⁿ. (2) Quotient rule: aᵐ ÷ aⁿ = aᵐ⁻ⁿ. (3) Power rule: (aᵐ)ⁿ = aᵐⁿ. (4) Zero exponent: a⁰ = 1. (5) Negative exponent: a⁻ⁿ = 1/aⁿ.
When do I use exponent rules?
Exponent rules show up in scientific notation, compound interest, population growth, radioactive half-life, computer science (binary), and simplifying algebraic expressions. They are foundational to exponential and logarithmic functions.

Related Topics

Power FunctionsExponential Growth & DecayLogarithmic Functions