Exponent Rules
Complete guide to exponent rules: product, quotient, power, zero, and negative exponents.
Simplify expressions with these essential rules.
The Rules
Product Rule: aᵐ × aⁿ = a^(m+n)
Quotient Rule: aᵐ ÷ aⁿ = a^(m-n)
Power Rule: (aᵐ)ⁿ = a^(m×n)
Zero Exponent: a⁰ = 1 (when a ≠ 0)
Negative Exponent: a⁻ⁿ = 1 / aⁿ
Distributive: (ab)ⁿ = aⁿ × bⁿ
Exponent rules let you simplify expressions involving powers.
They are fundamental to algebra and appear throughout mathematics and science.
Variables
| Symbol | Meaning |
|---|---|
| a, b | Base values (any non-zero number) |
| m, n | Exponents (any real numbers) |
Example 1
Simplify: 2³ × 2⁵
Using the Product Rule: aᵐ × aⁿ = a^(m+n)
2³ × 2⁵ = 2^(3+5) = 2⁸
2⁸ = 256
Example 2
Simplify: (3²)⁴ ÷ 3⁵
First apply the Power Rule: (3²)⁴ = 3^(2×4) = 3⁸
Then apply the Quotient Rule: 3⁸ ÷ 3⁵ = 3^(8-5) = 3³
3³ = 27
When to Use It
Use exponent rules when:
- Simplifying algebraic expressions with powers
- Multiplying or dividing terms with the same base
- Converting between negative exponents and fractions
- Working with scientific notation or very large/small numbers