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

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

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

Apply the Quotient of Powers Rule: When dividing powers with the same base, you subtract the exponents: x^m / x^n = x^(mn)
 For 'a': a^4 / a = a^(41) = a^3
 For 'b': b^4 / b^3 = b^(43) = b^1 = b

Combine the Results: The simplified expression is a^3 * b
Final Answer
Therefore, the simplified form of (ab)^4 / ab^3 is a^3b.