2 min read Jun 17, 2024

Simplifying the Expression (x^-4y/x^-9y^5)^-2

This article will guide you through simplifying the expression (x^-4y/x^-9y^5)^-2. Let's break down the steps using the rules of exponents.

Understanding the Properties of Exponents

To simplify the given expression, we need to recall the following properties of exponents:

  1. Product of Powers: x^m * x^n = x^(m+n)
  2. Quotient of Powers: x^m / x^n = x^(m-n)
  3. Power of a Power: (x^m)^n = x^(m*n)
  4. Negative Exponent: x^-n = 1/x^n

Simplifying the Expression

Let's simplify the expression step by step:

  1. Apply the Power of a Power rule: (x^-4y/x^-9y^5)^-2 = x^8y^-2 / x^18y^-10

  2. Apply the Quotient of Powers rule: x^8y^-2 / x^18y^-10 = x^(8-18)y^(-2-(-10))

  3. Simplify the exponents: x^(8-18)y^(-2-(-10)) = x^-10y^8

  4. Apply the Negative Exponent rule: x^-10y^8 = 1/x^10y^8

Therefore, the simplified form of (x^-4y/x^-9y^5)^-2 is 1/x^10y^8.


By applying the rules of exponents, we successfully simplified the given expression. Remember to always work through the steps systematically, using the appropriate properties to achieve the desired simplification.

Related Post

Featured Posts