What is the zero exponent rule?

Any non-zero base raised to the power 0 equals 1: a⁰ = 1 (when a ≠ 0).

What is the negative exponent rule?

a⁻ⁿ = 1/aⁿ. A negative exponent means the reciprocal. For example, 2⁻³ = 1/8.

Algebra

Laws of Exponents

Formula

aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ / aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ

What is Laws of Exponents?

The laws of exponents govern how to multiply, divide, and raise powers to powers. When multiplying like bases, add exponents. When dividing, subtract. When raising a power to a power, multiply.

Variables

a
a — Base
m
m, n — Exponents

Worked Examples

Example 1

Simplify x³ × x⁵.

Solution:

x³⁺⁵ = x⁸

Example 2

Simplify (x²)⁴.

Solution:

x²ˣ⁴ = x⁸

Example 3

Simplify x⁷ / x³.

Solution:

x⁷⁻³ = x⁴

Frequently Asked Questions

Related Formulas

Quadratic Equation

x = (−b ± √(b² − 4ac)) / 2a

Linear Equation in Two Variables

ax + by + c = 0

Distance Formula

Distance = Speed × Time

Factoring Quadratic Equations

ax² + bx + c = a(x − r₁)(x − r₂)

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