Three rules cover almost every exponent problem.
Quick check
Simplify x⁵ · x³ ÷ x²
Quick reference
- Zero power: x⁰ = 1 (for x ≠ 0).
- Power of a product: (xy)ⁿ = xⁿyⁿ.
- Power of a quotient: (x/y)ⁿ = xⁿ/yⁿ.
- These all fall out of the three core laws — multiply, divide, power-of-a-power.
Your turn
Simplify (2x²)³.
Watch out
x² · x³ is not x⁶. You add exponents when multiplying (giving x⁵); you only multiply them for a power of a power.
The three laws
- Multiply same base: xᵃ · xᵇ = xᵃ⁺ᵇ
- Divide same base: xᵃ / xᵇ = xᵃ⁻ᵇ
- Power of a power: (xᵃ)ᵇ = xᵃᵇ
Try it
x⁵ · x³
x⁸.
Try it
(x²)⁴
x⁸.