In this question, we are asked to simplify the expression (ab)(ab)(ab)(ab). Let's solve it step by step.
Step 1: Understand the Operations
The given expression represents a case of multiplication of four identical terms "(ab)". That's the same as raising the term "ab" to the power of 4. In other words, (ab)(ab)(ab)(ab) can be written as (ab)^4.
Step 2: Apply the Power of a Product Property
Remember the power of a product property, which says that the power of a product equals the product of each factor raised to the corresponding power. Thus, using this property, (ab)^4 can be written as (a^4)(b^4).
Step 3: Simplification
The expression (a^4)(b^4) is already simplified as it is. Hence, the simplified form of the given expression (ab)(ab)(ab)(ab) is a^4 * b^4.
So, the simplification of the given expression (ab)(ab)(ab)(ab) leads to the result a^4*b^4.