Product 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 Product of Powers Property is a rule in exponentiation that states:
Definition:
When you multiply two expressions with the same base and different exponents, you can add the exponents while keeping the base the same.
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 terms.
Example 1:
Example 2:
Explanation:
You add the exponents when multiplying like bases (the same base is repeated).
The base remains unchanged; only the exponents are combined.
This property is useful for simplifying expressions where you're multiplying terms with the same base, allowing you to condense the terms into a single expression with a combined exponent.