Exponent rules

Math

Definition

Exponent rules are properties that simplify expressions involving powers. They include rules for multiplying, dividing, and raising powers to powers, as well as handling zero and negative exponents.

Examples

  • x³ · x⁴ = x⁷ (product rule)
  • (2³)² = 2⁶ = 64 (power rule)
  • 5⁰ = 1 and x⁻² = 1/x² (zero and negative exponent rules)
Key Fact

xᵃ · xᵇ = xᵃ⁺ᵇ; xᵃ/xᵇ = xᵃ⁻ᵇ; (xᵃ)ᵇ = xᵃᵇ; x⁰ = 1; x⁻ⁿ = 1/xⁿ

Related Terms

Rational exponents Nth roots Polynomial operations Exponential growth and decay

Study This Concept

Practice exponent rules with free review games in these units:

Algebra 1 Unit 6: Exponents and Polynomials