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

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (2x³y²z²)^3(x²z)^4

This article will guide you through simplifying the expression (2x³y²z²)^3(x²z)^4. We will use the rules of exponents to achieve a simplified form.

Understanding the Rules of Exponents

To simplify this expression, we'll utilize the following rules of exponents:

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

Step-by-Step Simplification

1. Apply the Power of a Power rule to both terms:

   • (2x³y²z²)³ = 2³ * (x³)^3 * (y²)^3 * (z²)^3 = 8x⁹y⁶z⁶
   • (x²z)^4 = (x²)^4 * z^4 = x⁸z⁴

2. Combine the simplified terms using the Product of Powers rule:

   • 8x⁹y⁶z⁶ * x⁸z⁴ = 8x¹⁷y⁶z¹⁰

Final Answer

Therefore, the simplified form of the expression (2x³y²z²)^3(x²z)^4 is 8x¹⁷y⁶z¹⁰.