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(7xy^-2)^-2

less than a minute read Jun 16, 2024
(7xy^-2)^-2

Simplifying (7xy^-2)^-2

This expression involves several exponents and can be simplified using the rules of exponents. Here's how to break it down:

Understanding the Rules

  • Power of a Product: (ab)^n = a^n * b^n
  • Power of a Power: (a^m)^n = a^(m*n)
  • Negative Exponent: a^-n = 1/a^n

Applying the Rules

  1. Apply the Power of a Product Rule: (7xy^-2)^-2 = 7^-2 * x^-2 * (y^-2)^-2

  2. Apply the Power of a Power Rule: 7^-2 * x^-2 * (y^-2)^-2 = 7^-2 * x^-2 * y^4

  3. Apply the Negative Exponent Rule: 7^-2 * x^-2 * y^4 = 1/7^2 * 1/x^2 * y^4

  4. Simplify: 1/7^2 * 1/x^2 * y^4 = y^4 / 49x^2

Therefore, the simplified form of (7xy^-2)^-2 is y^4 / 49x^2.

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