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(x^-4y/x^-9y^5)^-2

2 min read Jun 17, 2024
(x^-4y/x^-9y^5)^-2

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.

Conclusion

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.

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