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(2xy)(3x^2y^4)/-6xy^5

2 min read Jun 16, 2024
(2xy)(3x^2y^4)/-6xy^5

Simplifying the Expression (2xy)(3x^2y^4)/-6xy^5

This article will guide you through the process of simplifying the expression (2xy)(3x^2y^4)/-6xy^5.

Understanding the Expression

The expression consists of multiplication and division of terms with variables and exponents. Here's a breakdown:

  • (2xy): This is a monomial with a coefficient of 2 and variables x and y, each with an exponent of 1.
  • (3x^2y^4): Another monomial with a coefficient of 3, x raised to the power of 2, and y raised to the power of 4.
  • -6xy^5: This is a monomial with a coefficient of -6, x raised to the power of 1, and y raised to the power of 5.

Simplifying the Expression

  1. Multiply the numerators: (2xy)(3x^2y^4) = 6x^(1+2)y^(1+4) = 6x^3y^5

  2. Combine the numerator and denominator: (6x^3y^5) / (-6xy^5)

  3. Simplify by dividing coefficients: 6 / -6 = -1

  4. Simplify by dividing variables: x^3 / x = x^(3-1) = x^2 y^5 / y^5 = y^(5-5) = y^0 = 1 (Any number raised to the power of 0 equals 1)

  5. Combine the simplified terms: -1 * x^2 * 1 = -x^2

Final Answer

Therefore, the simplified form of the expression (2xy)(3x^2y^4)/-6xy^5 is -x^2.

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