2 min read Jun 17, 2024

Simplifying Expressions with Exponents: (x^3y^2)^4(x^2y)

This article will guide you through simplifying the expression (x^3y^2)^4(x^2y). We will use the rules of exponents to break down the expression and arrive at a simplified form.

Understanding the Rules of Exponents

Before we dive into simplification, let's recap the relevant exponent rules:

  • Product of Powers: x^m * x^n = x^(m+n)
  • Power of a Power: (x^m)^n = x^(m*n)
  • Power of a Product: (x*y)^n = x^n * y^n

Simplifying the Expression

  1. Apply the Power of a Power rule: (x^3y^2)^4 = x^(34) * y^(24) = x^12 * y^8

  2. Rewrite the expression: Now our expression looks like this: x^12 * y^8 * x^2 * y

  3. Apply the Product of Powers rule: Combine the x terms and the y terms: x^(12+2) * y^(8+1) = x^14 * y^9

The Simplified Form

Therefore, the simplified form of (x^3y^2)^4(x^2y) is x^14y^9.

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