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(-2xy^3)(3x^6y^2)

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

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

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

Understanding the Basics

The expression involves multiplying two terms together. Both terms consist of numerical coefficients and variables with exponents.

  • Coefficients: These are the numerical factors in front of the variables. In our case, we have -2 and 3.
  • Variables: These are the letters representing unknown values. In our expression, we have x and y.
  • Exponents: These indicate the number of times a variable is multiplied by itself. For example, x^6 means x multiplied by itself six times.

Applying the Rules of Exponents

To simplify the expression, we need to apply the rules of exponents:

  • Multiplication of Powers with the Same Base: When multiplying powers with the same base, keep the base and add the exponents.
    • Example: x^m * x^n = x^(m+n)

Simplifying the Expression

  1. Multiply the coefficients: (-2) * (3) = -6

  2. Multiply the variables with the same base: x * x^6 = x^(1+6) = x^7 y^3 * y^2 = y^(3+2) = y^5

  3. Combine the results: (-6) * x^7 * y^5 = -6x^7y^5

Therefore, the simplified expression of (-2xy^3)(3x^6y^2) is -6x^7y^5.

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