FoundationsIntermediate
Working with Exponents and Powers
Exponents are just repeated multiplication — but a few simple rules let you combine and simplify them with ease.
Mathew JoaneJuly 28, 20266 min read
An exponent tells you how many times to multiply a base by itself. Writing 2⁴ is just shorthand for 2 × 2 × 2 × 2, which equals 16.
The core exponent rules
- Product rule: when multiplying like bases, add exponents — xᵃ × xᵇ = xᵃ⁺ᵇ.
- Quotient rule: when dividing like bases, subtract exponents — xᵃ ÷ xᵇ = xᵃ⁻ᵇ.
- Power rule: a power raised to a power multiplies exponents — (xᵃ)ᵇ = xᵃᵇ.
- Zero exponent: anything (except 0) to the power 0 is 1 — x⁰ = 1.
Seeing the rules in action
x³ × x² = x⁵
(x²)⁴ = x⁸
These rules become second nature with practice, and they are the foundation for scientific notation, exponential growth, and much of higher mathematics.
Written by Mathew Joane
Algebra teacher on a mission to make math feel less like memorizing and more like understanding.