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

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

Simplifying Algebraic Expressions: (3xy^3)(-4x^2y^4)^2(xy^3)

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

Understanding the Properties

To simplify this expression, we will make use of the following properties of exponents:

  • Product of powers: 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)

Step-by-Step Simplification

  1. Simplify the squared term: (-4x^2y^4)^2 = (-4)^2 * (x^2)^2 * (y^4)^2 = 16x^4y^8

  2. Combine the simplified terms: (3xy^3)(16x^4y^8)(xy^3)

  3. Multiply the coefficients: 3 * 16 * 1 = 48

  4. Apply the product of powers rule to the variables: x^(1+4+1) * y^(3+8+3) = x^6 * y^14

  5. Final simplified expression: 48x^6y^14

Conclusion

By applying the properties of exponents, we have successfully simplified the expression (3xy^3)(-4x^2y^4)^2(xy^3) to 48x^6y^14. Remember to always follow the order of operations and use the appropriate exponent rules to arrive at the correct simplified form.

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