In the property of a power of a product, what operation is performed on each factor?

In the property of a power of a product, when you have an expression of the form ( (ab)^n ), where ( a ) and ( b ) are factors and ( n ) is a power, what happens is that each factor is raised to the given power. This can be expressed with the equation ( (ab)^n = a^n \cdot b^n ).

This means that instead of simply multiplying the two factors together first, and then raising the result to the power, you separately raise each factor to that power and then multiply the results. This property is essential in simplifying expressions and solving equations efficiently, particularly when dealing with exponents in algebra.

Understanding this concept is pivotal in algebra, as it facilitates the manipulation of expressions involving exponents, allowing for more complex operations with greater ease.