(4a^3b/a^2b^3)(3b^2/2a^2b^4)

2 min read Jun 16, 2024
(4a^3b/a^2b^3)(3b^2/2a^2b^4)

Simplifying Algebraic Expressions: A Step-by-Step Guide

This article will guide you through the process of simplifying the algebraic expression: (4a^3b/a^2b^3)(3b^2/2a^2b^4).

Understanding the Basics

Before we begin simplifying, let's review some key concepts:

  • Exponents: An exponent indicates how many times a base number is multiplied by itself. For example, a^3 means a * a * a.
  • Fractions: When multiplying fractions, we multiply the numerators and the denominators separately.
  • Simplifying Expressions: We aim to reduce the expression to its simplest form by combining like terms and canceling out common factors.

Simplifying the Expression

  1. Multiply the Numerators:

    (4a^3b * 3b^2) = 12a^3b^3

  2. Multiply the Denominators:

    (a^2b^3 * 2a^2b^4) = 2a^4b^7

  3. Combine the Results:

    The simplified expression becomes: 12a^3b^3 / 2a^4b^7

  4. Simplify by Cancelling Common Factors:

    • Numbers: 12 and 2 share a common factor of 2.
    • Variables: a^3 and a^4 share a common factor of a^3.
    • Variables: b^3 and b^7 share a common factor of b^3.

    After canceling out common factors, the expression becomes: (6 * 1 * 1) / (1 * a * b^4) = 6 / ab^4

Final Answer

Therefore, the simplified form of the expression (4a^3b/a^2b^3)(3b^2/2a^2b^4) is 6/ab^4.

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