(2x^2y^3)^3/(2xy^2)^2

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (2x²y³)^3 / (2xy²)²

This article will guide you through the steps of simplifying the algebraic expression (2x²y³)^3 / (2xy²)².

Understanding the Properties

Before we begin simplifying, let's recall some important properties of exponents:

• Product of powers: (a^m)^n = a^(m*n)
• Quotient of powers: a^m / a^n = a^(m-n)

Simplifying the Expression

1. Apply the power of a power property:

   • (2x²y³)^3 = 2³(x²)³(y³)^3 = 8x⁶y⁹
   • (2xy²)^2 = 2²(x¹)²(y²)² = 4x²y⁴

2. Substitute the simplified terms back into the original expression:

   • (2x²y³)^3 / (2xy²)² = 8x⁶y⁹ / 4x²y⁴

3. Apply the quotient of powers property:

   • 8x⁶y⁹ / 4x²y⁴ = (8/4)x^(6-2)y^(9-4) = 2x⁴y⁵

Final Result

The simplified form of the expression (2x²y³)^3 / (2xy²)² is 2x⁴y⁵.