Algebra
Exponent Laws
All the rules for working with powers and exponents.
The Formula
aᵐ × aⁿ = aᵐ⁺ⁿ
Used for: Simplifying expressions with exponents/powers
aBase
m, nExponents (powers)
📋 Complete Exponent Laws
The six essential rules:
📐
aᵐ × aⁿ = aᵐ⁺ⁿProduct Rule: 2³ × 2⁴ = 2⁷ = 128
📐
aᵐ ÷ aⁿ = aᵐ⁻ⁿQuotient Rule: 3⁵ ÷ 3² = 3³ = 27
📐
(aᵐ)ⁿ = aᵐⁿPower Rule: (2³)² = 2⁶ = 64
📐
a⁰ = 1Zero Exponent: 5⁰ = 1
📐
a⁻ⁿ = 1/aⁿNegative Exponent: 2⁻³ = 1/8
📐
a^(1/n) = ⁿ√aFractional Exponent: 8^(1/3) = ∛8 = 2
📝 Worked Examples
Simplify Powers
Problem:
(2³ × 2⁵) ÷ 2⁴ = ?1
Multiply first
2³⁺⁵ ÷ 2⁴ = 2⁸ ÷ 2⁴2
Divide
2⁸⁻⁴ = 2⁴3
Calculate
2⁴ = 16Answer: 16
Negative Exponents
Problem:
Simplify: 3⁻² × 3⁵1
Add exponents
3⁻²⁺⁵2
Simplify
3³3
Calculate
= 27Answer: 27
💡 Pro Tips
Same base only!
Product and quotient rules only work when the BASE is the same
Negative ≠ negative number
2⁻³ = 1/8 (positive), not -8!
Order of operations
Evaluate exponents before multiplying: 2 × 3² = 2 × 9 = 18