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(5x^7y^-1)^-2

2 min read Jun 16, 2024
(5x^7y^-1)^-2

Simplifying the Expression: (5x^7y^-1)^-2

This article explores the process of simplifying the expression (5x^7y^-1)^-2.

Understanding the Properties of Exponents

Before we delve into the simplification, let's recall some key exponent properties:

  • 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)
  • Power of a Product: (x*y)^n = x^n * y^n
  • Power of a Quotient: (x/y)^n = x^n / y^n

Applying the Properties

Let's break down the simplification step-by-step:

  1. Apply the Power of a Power property:
    (5x^7y^-1)^-2 = 5^-2 * (x^7)^-2 * (y^-1)^-2

  2. Simplify each term: 5^-2 * (x^7)^-2 * (y^-1)^-2 = 1/5^2 * x^(7*-2) * y^(-1*-2) = 1/25 * x^-14 * y^2

  3. Express with positive exponents: 1/25 * x^-14 * y^2 = y^2 / (25x^14)

Final Result

Therefore, the simplified form of (5x^7y^-1)^-2 is y^2 / (25x^14).

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