%5E2.jpeg "(3x^3y^2)^2")
Simplifying (3x³y²)²
In mathematics, simplifying expressions is an essential skill. One common type of simplification involves raising a monomial to a power. Let's explore the steps to simplify the expression (3x³y²)².
Understanding the Power of a Product Rule
The key principle we'll use is the power of a product rule. This rule states that when a product is raised to a power, each factor within the product is raised to that power. Mathematically:
(ab)ⁿ = aⁿbⁿ
Applying the Rule
Let's apply this to our expression (3x³y²)²:
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Identify the factors: Our expression has three factors: 3, x³, and y².
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Apply the power of a product rule: Each factor is raised to the power of 2.
- (3)² = 9
- (x³)² = x⁶
- (y²)² = y⁴
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Combine the results: Multiplying the results of each factor, we get:
- 9x⁶y⁴
Final Answer
Therefore, the simplified form of (3x³y²)² is 9x⁶y⁴.
Key Takeaways
- The power of a product rule is a crucial tool for simplifying expressions with multiple factors raised to a power.
- Remember to apply the power to each individual factor within the product.
- Simplifying expressions involves breaking them down into their basic components and applying appropriate mathematical rules.