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What is an example of the power of a product rule?

Published in Exponents 1 min read

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.