Exponents Cheat Sheet

Exponent

The exponent tells you how many times to multiply the base by itself.

Example: In 2³, 3 is the exponent.

Base

The base is the number being multiplied by itself.

Example: In 2³, 2 is the base.

Power

A power is the result of raising a base to an exponent.

Example: 2³ = 8, so 8 is the power.

Product of Powers

When multiplying powers with the same base, add the exponents: aᵐ * aⁿ = aᵐ⁺ⁿ

Example: 2² * 2³ = 2²⁺³ = 2⁵ = 32

Quotient of Powers

When dividing powers with the same base, subtract the exponents: aᵐ / aⁿ = aᵐ⁻ⁿ

Example: 3⁵ / 3² = 3⁵⁻² = 3³ = 27

Power of a Power

When raising a power to another power, multiply the exponents: (aᵐ)ⁿ = aᵐ*ⁿ

Example: (2²)³ = 2²*³ = 2⁶ = 64

Power of a Product

A power of a product is the product of the powers: (ab)ⁿ = aⁿbⁿ

Example: (2x)³ = 2³x³ = 8x³

Power of a Quotient

A power of a quotient is the quotient of the powers: (a/b)ⁿ = aⁿ/bⁿ

Example: (x/3)² = x²/3² = x²/9

Zero Exponent

Any non-zero number raised to the power of 0 is 1: a⁰ = 1 (a ≠ 0)

Example: 5⁰ = 1

Negative Exponent

A negative exponent indicates a reciprocal: a⁻ⁿ = 1/aⁿ

Example: 2⁻² = 1/2² = 1/4

Exponent of 1

Any number raised to the power of 1 is itself: a¹ = a

Example: 7¹ = 7