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

Jasonbradley

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Jun 16, 2024

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

Let's break down the simplification of this expression step by step:

Understanding the Rules

• Exponents: When a term with an exponent is raised to another exponent, we multiply the exponents. For example, (x^m)^n = x^(m*n).
• Product of Powers: When multiplying terms with the same base, we add the exponents. For example, x^m * x^n = x^(m+n).

Applying the Rules

1. Simplify each term:

   • (3xy^3)^2 = 3^2 * x^2 * (y^3)^2 = 9x^2y^6
   • (-4x^2y^4)^2 = (-4)^2 * (x^2)^2 * (y^4)^2 = 16x^4y^8
   • (2xy^3) remains unchanged.

2. Multiply all terms together:

   • 9x^2y^6 * 16x^4y^8 * 2xy^3

3. Combine like terms:

   • (9 * 16 * 2) * (x^2 * x^4 * x) * (y^6 * y^8 * y^3)

4. Simplify:

   • 288x^7y^17

Final Answer

Therefore, the simplified form of the expression (3xy^3)^2(-4x^2y^4)^2(2xy^3) is 288x^7y^17.