Jasonbradley
Home

(-2u^-2v^2)^2*-2v^-5

2 min read Jun 16, 2024
(-2u^-2v^2)^2*-2v^-5

Simplifying the Expression (-2u^-2v^2)^2 * -2v^-5

This problem involves simplifying an expression with exponents. We will use the rules of exponents to achieve this.

Understanding the Rules of Exponents

  • Product of Powers: When multiplying powers with the same base, add the exponents. (x^m * x^n = x^(m+n))
  • Power of a Product: (xy)^n = x^n * y^n
  • Power of a Power: (x^m)^n = x^(m*n)
  • Negative Exponent: x^-n = 1/x^n

Applying the Rules

Let's simplify the expression step by step:

  1. Simplify the square: (-2u^-2v^2)^2 = (-2)^2 * (u^-2)^2 * (v^2)^2 = 4u^-4v^4

  2. Combine the terms: 4u^-4v^4 * -2v^-5 = -8u^-4 * v^(4-5)

  3. Simplify the exponent: -8u^-4 * v^-1

  4. Rewrite with positive exponents: -8u^-4 * v^-1 = -8 / (u^4 * v)

Final Result

The simplified form of the expression (-2u^-2v^2)^2 * -2v^-5 is -8 / (u^4 * v).

Related Post

Featured Posts