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Simplifying (a²b⁴c)³
In mathematics, simplifying expressions is a crucial skill. Let's explore how to simplify the expression (a²b⁴c)³.
Understanding the Problem
The expression (a²b⁴c)³ indicates that the entire expression within the parentheses (a²b⁴c) is multiplied by itself three times.
Applying the Rules of Exponents
To simplify, we'll utilize the following rules of exponents:
- Power of a Product: (xy)ⁿ = xⁿyⁿ
- Power of a Power: (xⁿ)ᵐ = xⁿᵐ
Step-by-Step Simplification
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Apply the Power of a Product rule: (a²b⁴c)³ = a²³ * b⁴³ * c³
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Apply the Power of a Power rule: a²³ * b⁴³ * c³ = a⁶ * b¹² * c³
Final Result
Therefore, the simplified expression for (a²b⁴c)³ is a⁶b¹²c³.
Key Takeaways
Simplifying expressions involves applying the appropriate rules of exponents. Understanding these rules allows us to express complex expressions in a more compact and manageable form.