(ab)^4/ab^3

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions: (ab)^4 / ab^3

This article will guide you through the process of simplifying the algebraic expression (ab)^4 / ab^3. We'll break down the steps and explain the underlying principles.

Understanding the Rules

Before we begin, let's recall some essential rules of exponents:

• Product of Powers: When multiplying powers with the same base, you add the exponents: x^m * x^n = x^(m+n)
• Power of a Power: When raising a power to another power, you multiply the exponents: (x^m)^n = x^(m*n)
• Power of a Product: When raising a product to a power, you apply the power to each factor: (xy)^n = x^n * y^n

Simplifying the Expression

1. Apply the Power of a Product Rule: (ab)^4 = a^4 * b^4

2. Rewrite the Expression: The expression becomes (a^4 * b^4) / (a * b^3)

3. Apply the Quotient of Powers Rule: When dividing powers with the same base, you subtract the exponents: x^m / x^n = x^(m-n)

   • For 'a': a^4 / a = a^(4-1) = a^3
   • For 'b': b^4 / b^3 = b^(4-3) = b^1 = b

4. Combine the Results: The simplified expression is a^3 * b

Final Answer

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