PanMaths.comFree Printable Math Formula Reference Sheet
Exponent Laws & Rules
Algebra • Grades 7, 8, 9, 10
Algebra
Exponent Laws & Rules
All the rules for working with powers and exponents.
The Formula
aᵐ × aⁿ = aᵐ⁺ⁿ
Used for: Simplifying algebraic expressions with powers, roots, and negative indices
aBase number or algebraic variable (a ≠ 0)
m, nExponents (positive, negative, or fractional powers)
⚡Live Interactive Quick Solver
Instant CalculationProduct Rule (2^3 × 2^4):2^7 = 128
Quotient: 2^-1 = 0.5000 • Power of Power: 2^12 = 4,096
a^m \cdot a^n = a^{m+n}, \quad \frac{a^m}{a^n} = a^{m-n}, \quad (a^m)^n = a^{m \cdot n}
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📋 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
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