Exponent rules simplify expressions with powers: Product (aᵐ×aⁿ = aᵐ⁺ⁿ), Quotient (aᵐ/aⁿ = aᵐ⁻ⁿ), Power ((aᵐ)ⁿ = aᵐⁿ), Zero (a⁰ = 1), Negative (a⁻ⁿ = 1/aⁿ), Fractional (a^(1/n) = ⁿ√a). These rules are the foundation of algebra and calculus.
How to Use
Select a rule and enter values:
- Base: The base number (a)
- Exponents: The power values (m, n)
- Result: Simplified expression
The Rules
- aᵐ × aⁿ = aᵐ⁺ⁿ (Product)
- aᵐ / aⁿ = aᵐ⁻ⁿ (Quotient)
- (aᵐ)ⁿ = aᵐⁿ (Power of Power)
- (ab)ⁿ = aⁿbⁿ (Product to Power)
- a⁰ = 1 (Zero Exponent)
- a⁻ⁿ = 1/aⁿ (Negative Exponent)
Common Mistakes
- aᵐ × bⁿ ≠ (ab)ᵐ⁺ⁿ — bases must be the same!
- (a+b)² ≠ a² + b² — must FOIL
- a⁻¹ ≠ −a — it means 1/a
Step-by-Step Instructions
- 1Select an exponent rule.
- 2Enter the base value.
- 3Enter the exponent values.
- 4View the simplified result.
- 5Check the step-by-step explanation.