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Simplifying (3x²y⁴)³
In mathematics, simplifying expressions is a fundamental skill. Let's break down how to simplify the expression (3x²y⁴)³.
Understanding the Rules
This expression involves exponents and parentheses. Here are the key rules to remember:
- Power of a product: (ab)ⁿ = aⁿbⁿ
- Power of a power: (aⁿ)ᵐ = aⁿᵐ
Step-by-Step Solution
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Apply the power of a product rule:
(3x²y⁴)³ = 3³(x²)³(y⁴)³
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Apply the power of a power rule:
3³(x²)³(y⁴)³ = 27x⁶y¹²
Final Result
The simplified form of (3x²y⁴)³ is 27x⁶y¹².
Key Takeaways
- The power of a product rule allows us to distribute the exponent to each factor within the parentheses.
- The power of a power rule tells us to multiply the exponents when raising a power to another power.
By understanding these rules and applying them systematically, we can simplify complex expressions like (3x²y⁴)³ and arrive at a concise and clear result.