Jasonbradley
Home

(4ab^-5)^-2

2 min read Jun 16, 2024
(4ab^-5)^-2

Simplifying (4ab^-5)^-2

This article will guide you through the process of simplifying the expression (4ab^-5)^-2.

Understanding the Rules

To simplify this expression, we need to utilize a few key rules of exponents:

  • Product 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. Distribute the exponent: Apply the power of a power rule to each term within the parentheses: (4ab^-5)^-2 = 4^-2 * a^-2 * (b^-5)^-2

  2. Simplify the exponents: Multiply the exponents together: 4^-2 * a^-2 * (b^-5)^-2 = 4^-2 * a^-2 * b^10

  3. Apply the negative exponent rule: Move terms with negative exponents to the denominator: 4^-2 * a^-2 * b^10 = (b^10) / (4^2 * a^2)

  4. Simplify the expression: Calculate the value of 4^2: (b^10) / (4^2 * a^2) = b^10 / 16a^2

Final Result

Therefore, the simplified expression of (4ab^-5)^-2 is b^10 / 16a^2.

Related Post

Featured Posts