(3b%5E2%2F2a%5E2b%5E4).jpeg "(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
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Multiply the Numerators:
(4a^3b * 3b^2) = 12a^3b^3
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Multiply the Denominators:
(a^2b^3 * 2a^2b^4) = 2a^4b^7
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Combine the Results:
The simplified expression becomes: 12a^3b^3 / 2a^4b^7
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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.