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(2x^3y^-3)^-2

2 min read Jun 16, 2024
(2x^3y^-3)^-2

Simplifying the Expression: (2x^3y^-3)^-2

This article will guide you through simplifying the expression (2x^3y^-3)^-2. We will use the rules of exponents to reach a simplified form.

Understanding the Rules of Exponents

Before diving into the simplification, let's recall the relevant rules of exponents:

  • Product of powers: x^m * x^n = x^(m+n)
  • Quotient of powers: x^m / x^n = x^(m-n)
  • Power of a power: (x^m)^n = x^(m*n)
  • Negative exponent: x^-n = 1/x^n

Simplifying the Expression

  1. Distribute the outer exponent: Applying the power of a power rule, we distribute the -2 exponent to each term within the parentheses: (2x^3y^-3)^-2 = 2^-2 * (x^3)^-2 * (y^-3)^-2

  2. Simplify each term:

    • 2^-2 = 1/2^2 = 1/4
    • (x^3)^-2 = x^(3*-2) = x^-6
    • (y^-3)^-2 = y^(-3*-2) = y^6

  3. Combine the terms: 1/4 * x^-6 * y^6 = (1/4) * (1/x^6) * y^6 = y^6 / (4x^6)

Final Result

Therefore, the simplified form of (2x^3y^-3)^-2 is y^6 / (4x^6).

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