%5E4.jpeg "(3a^2)^4")
Simplifying (3a^2)^4
In mathematics, simplifying expressions is crucial for understanding their value and manipulating them effectively. One common expression that arises is (3a^2)^4. Let's break down how to simplify this expression.
Understanding the Rules
To simplify this expression, we need to recall two fundamental rules of exponents:
- Power of a product: (ab)^n = a^n * b^n
- Power of a power: (a^m)^n = a^(m*n)
Applying the Rules
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Apply the power of a product rule: (3a^2)^4 = 3^4 * (a^2)^4
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Apply the power of a power rule: 3^4 * (a^2)^4 = 81 * a^(2*4)
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Simplify the expression: 81 * a^(2*4) = 81a^8
Final Result
Therefore, the simplified form of (3a^2)^4 is 81a^8.
Key Takeaways
- Understanding the rules of exponents is essential for simplifying complex expressions.
- Applying the rules step-by-step helps avoid errors and ensures a clear understanding of the process.
- Simplification makes expressions easier to work with and allows for easier comparison and analysis.