1. If one factor is expanded or reduced by n times (n is a non-zero natural number) and the other factor remains unchanged, then their product is also expanded or reduced by n times.

2. If one factor is magnified a times and the other factor is magnified b times, their product will be magnified a*b times.

3. If one factor is enlarged by n times and the other factor is reduced by n times, their product remains unchanged.

Product is a concept of category theory, such as multiplication of two integers and inner product of two vectors in vector space. In mathematics, product refers to the result of multiplication of two or more numbers. The sign of the product is the multiplication sign (×), for example, 2×3=6, where 2 and 3 are multiplicand and 6 is the product. Product is a basic concept and one of the most basic operations in mathematics.

Product can be used to represent the product of multiple identical factors, and it can also be used to represent the product of different factors. For example, 4×4×4 can be written as 4 3, where 4 is a factor, 3 is an exponent, and 4 3 represents the cube of 4. Similarly, 2×3×5 can be written as 2×3×5, where 2, 3 and 5 are different factors.

Products are widely used in mathematics, such as algebra, geometry, calculus, probability and other branches of mathematics. In algebra, product is the result of polynomial multiplication; In geometry, product is one of the basic methods to calculate area and volume. In calculus, product is one of the basic tools to solve definite integral and differential equations. In probability theory, product is one of the calculation methods of joint probability and conditional probability.

Arithmetic of product in mathematics;

The arithmetic rules of product in mathematics include sign rule, exponent rule, zero rule and reciprocal rule. Symbolic rules mean that positive numbers are multiplied by positive numbers, negative numbers are multiplied by negative numbers, and 0 is multiplied by any number; Exponential law means that the exponent of the product is equal to the sum of the exponents of the factors, such as a m× a n = a (m+n).

The zero rule means that any number is multiplied by 0 to get 0; The reciprocal rule means that the reciprocal of a number and its product is equal to 1, that is, a× 1/a= 1. These operation rules are the basic rules of product operation in mathematics and are widely used. Product has some basic properties in mathematics, such as associative law, commutative law and distributive law. The law of association means that the order of products does not affect the results of products.