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(3xy^2)(2x2y^3)

2 min read Jun 16, 2024
(3xy^2)(2x2y^3)

Simplifying Expressions: (3xy^2)(2x^2y^3)

This article will guide you through simplifying the expression (3xy^2)(2x^2y^3).

Understanding the Basics

Before we dive into the simplification, let's clarify some fundamental concepts:

  • Coefficients: Numbers that multiply variables (e.g., 3, 2 in the expression).
  • Variables: Symbols representing unknown values (e.g., x, y).
  • Exponents: Numbers indicating how many times a variable is multiplied by itself (e.g., 2 in x^2, meaning x * x).

Applying the Rules

To simplify the expression, we'll use the following rules:

  1. Commutative Property: The order of multiplication doesn't change the result.
  2. Associative Property: Grouping of multiplication doesn't affect the result.
  3. Product of Powers: When multiplying powers with the same base, add their exponents.

Simplifying the Expression

Let's break down the steps:

  1. Rearrange terms: We can rearrange the terms using the commutative property: (3 * 2) * (x * x^2) * (y^2 * y^3)

  2. Multiply coefficients: 6 * (x * x^2) * (y^2 * y^3)

  3. Apply the Product of Powers rule: 6 * x^(1+2) * y^(2+3)

  4. Simplify: 6x^3y^5

Final Result

The simplified form of (3xy^2)(2x^2y^3) is 6x^3y^5.

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