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

Jasonbradley

2 min read

·

Jun 16, 2024

21

Share

Simplifying Expressions with Exponents

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

Understanding the Rules

Before we dive into the simplification, let's review some key rules 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)

Applying the Rules

1. Distribute the exponents:

   • (-2xy^2)^4 = (-2)^4 * x^4 * (y^2)^4 = 16x^4y^8
   • (2x^3y^4)^2 = 2^2 * (x^3)^2 * (y^4)^2 = 4x^6y^8

2. Multiply the resulting terms:

   • 16x^4y^8 * 4x^6y^8 = 64x^(4+6)y^(8+8) = 64x^10y^16

The Final Answer

Therefore, the simplified form of (-2xy^2)^4(2x^3y^4)^2 is 64x^10y^16.

Conclusion

By applying the rules of exponents, we successfully simplified the complex expression. Remember to always break down the problem into smaller steps and use the appropriate rules for each step. This approach ensures accuracy and helps you avoid common errors.