7 Rules for Exponents with Examples | Livius Tutoring (2024)

November 29, 2021

Exponents can be a tricky subject to master – all these numbers raised to more numbers divided by other numbers and multiplied by the power of another number. What?! Confusing much?In this article, we’ll review 7 KEY Rules for Exponents along with an example of each. For each rule, we’ll give you the name of the rule, a definition of the rule, and a real example of how the rule will be applied.

For all examples below, assume that X and Y are nonzero real numbers and a and b are integers.

RULE 1: Zero Property

Definition: Any nonzero real number raised to the power of zero will be 1.

Example:

RULE 2: Negative Property

Definition: Any nonzero real number raised to a negative power will be one divided by the number raised to the positive power of the same number.

Example:

RULE 3: Product Property

Definition: When multiplying two exponents with the same nonzero real number base, the answer will be the sum of the exponents with the same base

Example:

RULE 4: Quotient Property

Definition: When dividing two exponents with the same nonzero real number base, the answer will be the difference of the exponents with the same base.

Example:

RULE 5: Power of a Power Property

Definition: If an exponent is raised to another exponent, you can multiply the exponents.

Example:

RULE 6: Power of a Product Property

Definition: If the product of two nonzero real numbers is being raised to an exponent, you can distribute the exponent to each factor and multiply individually.

Example:

RULE 7: Power of a Quotient Property

Definition: If the quotient of two nonzero real numbers are being raised to an exponent, you can distribute the exponent to each individual factor and divide individually.

Example:

Next time you’re faced with a challenging exponent question, keep these rules in mind and you’ll be sure to succeed!