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(4x^5y^3/3xy^5)^2

3 min read Jun 16, 2024
(4x^5y^3/3xy^5)^2

Simplifying the Expression: (4x^5y^3/3xy^5)^2

This article will guide you through simplifying the expression (4x^5y^3/3xy^5)^2. We will use the rules of exponents and fraction simplification to arrive at the most simplified form.

Understanding the Expression

The expression represents a fraction raised to the power of 2. To simplify, we need to consider the following rules:

  • Power of a fraction: (a/b)^n = a^n / b^n
  • Power of a product: (ab)^n = a^n * b^n
  • Division of powers with the same base: a^m / a^n = a^(m-n)

Step-by-Step Simplification

  1. Apply the power of a fraction rule: (4x^5y^3/3xy^5)^2 = (4x^5y^3)^2 / (3xy^5)^2

  2. Apply the power of a product rule to both numerator and denominator: (4x^5y^3)^2 / (3xy^5)^2 = (4^2 * (x^5)^2 * (y^3)^2) / (3^2 * x^2 * (y^5)^2)

  3. Simplify the powers: (4^2 * (x^5)^2 * (y^3)^2) / (3^2 * x^2 * (y^5)^2) = (16x^10y^6) / (9x^2y^10)

  4. Apply the division of powers with the same base rule: (16x^10y^6) / (9x^2y^10) = (16/9) * x^(10-2) * y^(6-10)

  5. Simplify further: (16/9) * x^(10-2) * y^(6-10) = (16/9)x^8y^-4

Final Simplified Form

The simplified form of the expression (4x^5y^3/3xy^5)^2 is (16/9)x^8y^-4. We can also express it as (16x^8) / (9y^4), depending on the desired format.

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