An example of the power of a product rule is simplifying an expression where a product of terms is raised to a power. According to the reference, the power of a product rule deals with "raising the product a*b*c to the power of n results in the power of a product (a*b*c)^n". Let's break this down with a specific example.
Example:
Consider the expression (2x*y)^3. This represents the product of 2, x, and y, all raised to the power of 3. Applying the power of a product rule, we distribute the exponent to each factor within the parentheses.
(2x*y)^3 = 2^3 * x^3 * y^3 = 8x^3y^3
Here's a table summarizing the steps:
Step | Explanation | Example |
---|---|---|
1. Identify the product raised to a power. | Recognize the expression in the form (a*b*c)^n | (2x*y)^3 |
2. Distribute the exponent to each factor. | Apply the exponent 'n' to each individual term a, b, and c. | 2^3 * x^3 * y^3 |
3. Simplify. | Calculate and rewrite the expression. | 8x^3y^3 |
Therefore, the expression (2xy)^3 simplifies to 8x^3y^3 using the power of a product rule. This rule provides a method for simplifying complex expressions.