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

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (3x³y²)^3(2x⁴y²)^2

This article will guide you through simplifying the expression (3x³y²)^3(2x⁴y²)^2. We'll break down the steps using the properties of exponents.

Understanding the Properties of Exponents

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

• 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. Distribute the exponents:

   • (3x³y²)^3 = 3³ * (x³)^3 * (y²)^3 = 27x⁹y⁶
   • (2x⁴y²)^2 = 2² * (x⁴)² * (y²)² = 4x⁸y⁴

2. Multiply the simplified terms:

   • 27x⁹y⁶ * 4x⁸y⁴ = (27 * 4) * (x⁹ * x⁸) * (y⁶ * y⁴)

3. Apply the Product of Powers property:

   • 108x¹⁷y¹⁰

Final Answer

Therefore, the simplified expression is 108x¹⁷y¹⁰.