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

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

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

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.