Exponent Rules: Product, Quotient, Power and Zero
Learn the exponent rules for multiplying, dividing and raising powers, plus the zero exponent, with worked examples and a common mistake.
The four rules
- Product: xᵃ · xᵇ = xᵃ⁺ᵇ
- Quotient: xᵃ / xᵇ = xᵃ⁻ᵇ
- Power: (xᵃ)ᵇ = xᵃᵇ
- Zero: x⁰ = 1 (x ≠ 0)
Same base: add when multiplying, subtract when dividing.
Power of a power
- (x²)⁵ = x²ˣ⁵ = x¹⁰
- Multiply the exponents
- Do not add them
Add for a product. Multiply for a power.
Example 1
Simplify x³ · x⁴
- Same base, multiplying
- Add the exponents: 3 + 4
x⁷
Example 2
Simplify (x²)⁵
- A power of a power
- Multiply the exponents: 2 × 5
x¹⁰
Common mistake
(x + y)² = x² + y²
Squaring a sum is (x + y)(x + y), not two separate squares.
The correct expansion is x² + 2xy + y².
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