(3a^2b-6ab+5ab^2)(ab)^-1

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions: (3a²b - 6ab + 5ab²)(ab)⁻¹

This article will walk through the process of simplifying the algebraic expression (3a²b - 6ab + 5ab²)(ab)⁻¹.

Understanding the Concepts

Before we start simplifying, let's understand the key concepts involved:

• Exponent Rule: When a term with an exponent is raised to another exponent, we multiply the exponents. For example: (x^m)^n = x^(m*n).
• Negative Exponent Rule: A term with a negative exponent is equal to its reciprocal with a positive exponent. For example: x⁻¹ = 1/x.

Simplifying the Expression

1. Simplify (ab)⁻¹: Applying the negative exponent rule, we get: (ab)⁻¹ = 1/(ab).

2. Rewrite the Expression: Now, our expression becomes: (3a²b - 6ab + 5ab²)(1/ab)

3. Multiply each term by 1/(ab): This results in:

   • (3a²b * 1/ab) - (6ab * 1/ab) + (5ab² * 1/ab)

4. Simplify by cancelling common factors:

   • (3a²/a) - (6b/b) + (5ab/a)

5. Final Simplified Expression: The simplified expression is: 3a - 6 + 5b

Conclusion

We have successfully simplified the expression (3a²b - 6ab + 5ab²)(ab)⁻¹ to 3a - 6 + 5b by applying basic exponent rules and simplifying the expression step-by-step. Remember to always work carefully and follow the order of operations for accurate results.