(x^2y^4z)^5/(xy)^2

Jasonbradley

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Jun 17, 2024

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Simplifying Algebraic Expressions: (x^2y^4z)^5/(xy)^2

This article will guide you through the process of simplifying the algebraic expression (x^2y^4z)^5/(xy)^2. We'll use the properties of exponents to break down the expression step-by-step.

Understanding the Properties of Exponents

Before we begin, let's recall some key properties of exponents:

• Power of a Product: (ab)^n = a^n * b^n
• Power of a Power: (a^m)^n = a^(m*n)
• Division of Powers with the Same Base: a^m / a^n = a^(m-n)

Simplifying the Expression

1. Apply the Power of a Product rule:

   (x^2y^4z)^5 = x^(25) * y^(45) * z^5 = x^10 * y^20 * z^5

   (xy)^2 = x^(12) * y^(12) = x^2 * y^2

2. Rewrite the original expression:

   (x^2y^4z)^5/(xy)^2 = (x^10 * y^20 * z^5) / (x^2 * y^2)

3. Apply the Division of Powers with the Same Base rule:

   x^10 / x^2 = x^(10-2) = x^8 y^20 / y^2 = y^(20-2) = y^18

4. Combine the simplified terms:

   (x^10 * y^20 * z^5) / (x^2 * y^2) = x^8 * y^18 * z^5

Final Simplified Expression

Therefore, the simplified form of (x^2y^4z)^5/(xy)^2 is x^8y^18z^5.