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

less than a minute read Jun 16, 2024
(2x^2y^3)^3/(2xy^2)^2

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.

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