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Simplifying Expressions with Exponents
This article will guide you through simplifying the expression (4x⁴y)² * 2x³y⁴. We'll break down the steps using the rules of exponents.
Understanding the Rules of Exponents
Before we begin, let's review the key rules of exponents that we'll use:
- 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)
Simplifying the Expression
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Apply the Power of a Product rule to the first term: (4x⁴y)² = 4² * (x⁴)² * y² = 16x⁸y²
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Now we have: 16x⁸y² * 2x³y⁴
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Apply the Product of Powers rule for x and y terms: 16x⁸y² * 2x³y⁴ = (16 * 2) * (x⁸ * x³) * (y² * y⁴)
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Simplify further: 32x¹¹y⁶
Final Answer
Therefore, the simplified expression for (4x⁴y)² * 2x³y⁴ is 32x¹¹y⁶.