Quotient of Powers 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 Quotient of Powers Property is a rule in exponentiation that applies when you divide two expressions with the same base and different exponents. It states:
Definition:
When you divide two expressions that have the same base, you subtract the exponent of the denominator from the exponent of the numerator.
Key Points:
a is the base (it can be any number, variable, or expression),
m and n are the exponents,
The base a must be the same in both the numerator and the denominator.
Example 1:
Example 2:
Explanation:
You subtract the exponents: the exponent of the denominator is subtracted from the exponent of the numerator.
The base remains the same, and only the exponents are combined.
This property helps simplify expressions involving division of powers with the same base, turning them into a single expression with a new exponent.