(3x^2y^4)(4xy^2) In Simplest Form

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (3x²y⁴)(4xy²)

This expression involves multiplying two monomials, where a monomial is a single term consisting of a coefficient and one or more variables with exponents. To simplify this, we use the following rules:

• Product of Powers Rule: When multiplying powers with the same base, add their exponents.
  • Example: x² * x³ = x⁵
• Commutative Property: The order of multiplication doesn't matter.
  • Example: 3 * 4 = 4 * 3

Step 1: Rearrange the terms using the Commutative Property:

(3x²y⁴)(4xy²) = 3 * 4 * x² * x * y⁴ * y²

Step 2: Apply the Product of Powers Rule:

3 * 4 * x² * x * y⁴ * y² = 12 * x³ * y⁶

Therefore, the simplest form of (3x²y⁴)(4xy²) is 12x³y⁶.