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

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions with Exponents

This article will guide you through simplifying the expression (4x^4y)^2 x 2x^3y^4. We will use the rules of exponents to achieve a clear and concise result.

Understanding the Rules of Exponents

Before we start simplifying, let's review the essential 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)

Step-by-Step Simplification

1. Apply the power of a product rule to the first term: (4x^4y)^2 = 4^2 * (x^4)^2 * y^2 = 16x^8y^2

2. Combine the simplified first term with the second term: 16x^8y^2 * 2x^3y^4

3. Apply the product of powers rule: 16 * 2 * x^(8+3) * y^(2+4) = 32x^11y^6

Final Result

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

Remember to always follow the order of operations and apply the correct rules of exponents to simplify expressions effectively.