2 min read Jun 17, 2024

Simplifying (xy^-6)^2

In mathematics, simplifying expressions often involves applying rules of exponents. Let's break down how to simplify the expression (xy^-6)^2.

Understanding the Rules

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

Applying the Rules

  1. Distribute the exponent: Using the power of a product rule, we can distribute the exponent '2' to both 'x' and 'y^-6': (xy^-6)^2 = x^2 * (y^-6)^2

  2. Simplify the power of a power: Applying the power of a power rule, we multiply the exponents of 'y': x^2 * (y^-6)^2 = x^2 * y^(-6*2) = x^2 * y^-12

  3. Rewrite with positive exponents: We can rewrite y^-12 with a positive exponent by moving it to the denominator: x^2 * y^-12 = x^2 / y^12

Final Result

Therefore, the simplified form of (xy^-6)^2 is x^2 / y^12.