(4x^4y)^2*2x^3y^4

Jasonbradley

2 min read

·

Jun 16, 2024

17

Share

Simplifying Expressions with Exponents

This article will guide you through simplifying the expression (4x⁴y)² * 2x³y⁴. We'll break down the steps using the rules of exponents.

Understanding the Rules of Exponents

Before we begin, let's review the key rules of exponents that we'll use:

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

Simplifying the Expression

1. Apply the Power of a Product rule to the first term: (4x⁴y)² = 4² * (x⁴)² * y² = 16x⁸y²

2. Now we have: 16x⁸y² * 2x³y⁴

3. Apply the Product of Powers rule for x and y terms: 16x⁸y² * 2x³y⁴ = (16 * 2) * (x⁸ * x³) * (y² * y⁴)

4. Simplify further: 32x¹¹y⁶

Final Answer

Therefore, the simplified expression for (4x⁴y)² * 2x³y⁴ is 32x¹¹y⁶.