%5E3.jpeg "(6x^4y^6)^3")
Simplifying the Expression (6x⁴y⁶)³
This article will guide you through the process of simplifying the expression (6x⁴y⁶)³.
Understanding the Concept
The expression (6x⁴y⁶)³ signifies that the entire term inside the parentheses, 6x⁴y⁶, is being multiplied by itself three times. This is a case of applying the power of a product rule in algebra, which states:
(ab)ⁿ = aⁿbⁿ
Applying the Rule
Let's break down the simplification step-by-step:
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Apply the power of a product rule: (6x⁴y⁶)³ = 6³(x⁴)³(y⁶)³
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Simplify each term: 6³ = 216 (x⁴)³ = x¹² (remember, when raising a power to another power, you multiply the exponents) (y⁶)³ = y¹⁸
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Combine the simplified terms: 216x¹²y¹⁸
Final Result
Therefore, the simplified form of (6x⁴y⁶)³ is 216x¹²y¹⁸.
Key Takeaways
- The power of a product rule is essential for simplifying expressions with multiple terms raised to a power.
- Remember to apply the power to each individual term within the parentheses.
- Multiply exponents when raising a power to another power.