a×a×b×b

a×a×b×b is a mathematical expression representing the product of four numbers. It can be simplified using the properties of exponents. Specifically, the repeated multiplication of a by itself is denoted as a squared, or a^2. Similarly, the repeated multiplication of b by itself is denoted as b squared, or b^2. Therefore, the expression a×a×b×b can be rewritten as a^2 × b^2. This simplified form is often used in algebra and other areas of mathematics.

The expression a^2 × b^2 has further properties. According to the rules of exponents, when two terms are squared and then multiplied, they can be combined into a single term squared. This means that a^2 × b^2 is equivalent to (a × b)^2, or (ab)^2. This identity is known as the power of a product rule. It states that the power of a product is equal to the product of the powers of each factor. The expression (ab)^2 represents the square of the product of a and b.

In essence, a×a×b×b is a compact way of representing the square of the product of two variables, a and b. It is a fundamental building block in algebraic manipulation and simplification. Understanding this expression is key to grasping more complex algebraic concepts.