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(-x^5y^7)^2/(2x^2y^3)^4

2 min read Jun 16, 2024
(-x^5y^7)^2/(2x^2y^3)^4

Simplifying Algebraic Expressions: (-x^5y^7)^2/(2x^2y^3)^4

This article will guide you through simplifying the algebraic expression (-x^5y^7)^2/(2x^2y^3)^4.

Understanding the Rules

To simplify this expression, we need to utilize the following rules of exponents:

  • Power of a product: (ab)^n = a^n * b^n
  • Power of a quotient: (a/b)^n = a^n / b^n
  • Power of a power: (a^m)^n = a^(m*n)

Step-by-Step Simplification

  1. Apply the Power of a Product Rule:

    • (-x^5y^7)^2 = (-1)^2 * (x^5)^2 * (y^7)^2 = x^10y^14
    • (2x^2y^3)^4 = 2^4 * (x^2)^4 * (y^3)^4 = 16x^8y^12

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

    • (x^10y^14) / (16x^8y^12)

  3. Apply the Power of a Quotient Rule:

    • (x^10 / 16x^8) * (y^14 / y^12)

  4. Simplify using the rule for dividing exponents with the same base:

    • (x^(10-8) / 16) * (y^(14-12))
    • (x^2 / 16) * (y^2)

Final Result

Therefore, the simplified form of the expression (-x^5y^7)^2/(2x^2y^3)^4 is x^2y^2 / 16.

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