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(2x^2y^3)(4xy^-2)

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

Simplifying the Expression (2x^2y^3)(4xy^-2)

This article will guide you through the process of simplifying the algebraic expression (2x^2y^3)(4xy^-2).

Understanding the Basics

Before we start simplifying, let's recall some fundamental rules of exponents:

  • Product of powers: When multiplying exponents with the same base, add the powers. For example, x^m * x^n = x^(m+n)
  • Negative exponents: A term raised to a negative exponent is equal to its reciprocal raised to the positive version of the exponent. For example, x^-n = 1/x^n

Simplifying the Expression

  1. Rearrange the terms: It's helpful to rearrange the expression to group like terms together. (2x^2y^3)(4xy^-2) = (2 * 4) (x^2 * x) (y^3 * y^-2)

  2. Apply the product of powers rule: (2 * 4) (x^2 * x) (y^3 * y^-2) = 8x^(2+1)y^(3-2)

  3. Simplify the exponents: 8x^(2+1)y^(3-2) = 8x^3y^1

  4. Final simplified form: 8x^3y^1 = 8x^3y

Therefore, the simplified form of (2x^2y^3)(4xy^-2) is 8x^3y.

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