(4x^4y)^2 Times 2x^3y^4

Jasonbradley

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Jun 16, 2024

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

This article will guide you through simplifying the expression (4x^4y)^2 * 2x^3y^4. We'll use the rules of exponents to break down the problem step-by-step.

Understanding the Rules

Before we begin, let's recall the key rules of exponents we'll be using:

• Power of a product: (ab)^n = a^n * b^n
• Product of powers: a^m * a^n = a^(m+n)

Applying the Rules

1. Simplify the first term (4x^4y)^2:

   • Using the power of a product rule, we get: (4x^4y)^2 = 4^2 * (x^4)^2 * y^2
   • Simplifying further: 16x^8y^2

2. Combine the simplified first term with the second term:

   • Our expression now looks like this: 16x^8y^2 * 2x^3y^4

3. Multiply the coefficients:

   • 16 * 2 = 32

4. Apply the product of powers rule to the variables:

   • x^8 * x^3 = x^(8+3) = x^11
   • y^2 * y^4 = y^(2+4) = y^6

The Final Result

Therefore, the simplified form of the expression (4x^4y)^2 * 2x^3y^4 is 32x^11y^6.