7 Rules for Exponents with Examples
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.
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.
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
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.
RULE 5: Power of a Power Property
Definition: If an exponent is raised to another exponent, you can multiply the exponents.
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.
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.
Next time you’re faced with a challenging exponent question, keep these rules in mind and you’ll be sure to succeed!