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CalcVerse🔣 AlgebraExponent Rules

Exponent Rules

Six exponent laws with examples and a cheat sheet

Grades 7–9

Exponent Rules

Apply and simplify exponent rule expressions step by step

General Rule
aᵐ × aⁿ = aᵐ⁺ⁿ
Steps
Step 1: Apply Product Rule
3² × 3⁴ = 3²⁺⁴
Step 2: Add Exponents
= 3⁶
Step 3: Evaluate
= 729
Result
3⁶ = 729
Quick Reference — All 6 Rules
Product Rule
aᵐ × aⁿ = aᵐ⁺ⁿe.g. 2³ × 2⁴ = 2⁷ = 128
Quotient Rule
aᵐ / aⁿ = aᵐ⁻ⁿe.g. 5⁶ / 5² = 5⁴ = 625
Power Rule
(aᵐ)ⁿ = aᵐˣⁿe.g. (3²)⁴ = 3⁸ = 6561
Zero Exponent
a⁰ = 1e.g. 99⁰ = 1
Negative Exponent
a⁻ⁿ = 1/aⁿe.g. 2⁻³ = 1/8 = 0.125
Product to Power
(ab)ⁿ = aⁿ × bⁿe.g. (2·3)³ = 8×27 = 216