Jasonbradley
Home

(2y^4/y^3)^-2

2 min read Jun 16, 2024
(2y^4/y^3)^-2

Simplifying Expressions with Exponents: (2y^4/y^3)^-2

This article will guide you through the process of simplifying the expression (2y^4/y^3)^-2. We will utilize the properties of exponents to break down the problem into manageable steps.

Understanding the Properties of Exponents

Before diving into the problem, let's review some fundamental exponent rules:

  • 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)
  • Negative exponent: x^-n = 1/x^n

Step-by-Step Simplification

  1. Simplify inside the parentheses:

    • (2y^4 / y^3) = 2y^(4-3) = 2y

  2. Apply the power of a power rule:

    • (2y)^-2 = 2^-2 * y^-2

  3. Apply the negative exponent rule:

    • 2^-2 * y^-2 = 1/2^2 * 1/y^2

  4. Simplify:

    • 1/2^2 * 1/y^2 = 1/4 * 1/y^2 = 1/(4y^2)

Conclusion

Therefore, the simplified form of (2y^4/y^3)^-2 is 1/(4y^2). By carefully applying the properties of exponents, we were able to break down the complex expression into a simpler, more manageable form. Remember to practice these rules to become proficient in simplifying expressions with exponents.

Featured Posts