Power of a Quotient Property
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
The Power of a Quotient Property is a rule in exponentiation that deals with raising a quotient (a fraction) to an exponent. The property states that:
Definition:
When a fraction (quotient) is raised to an exponent, the exponent applies to both the numerator and the denominator separately.
Key Points:
a and b are any numbers, variables, or expressions (with b not equal to 0),
n is the exponent.
The exponent is distributed to both the numerator and the denominator.
Example 1:
Example 2:
This property is helpful when simplifying expressions involving exponents and fractions, as it allows you to separate the powers in the numerator and denominator for easier calculation or further simplification.