%5E2.jpeg "(3a^2)^2")
Simplifying (3a^2)^2
In mathematics, simplifying expressions is a crucial skill. One common expression that can be simplified is (3a^2)^2. Let's break down the steps to simplify this expression:
Understanding the Properties
The expression (3a^2)^2 involves the following key concepts:
- Exponents: An exponent indicates how many times a base is multiplied by itself. In this case, we have a base of 3a^2, and it is raised to the power of 2.
- Order of Operations: We follow the order of operations (PEMDAS/BODMAS) to simplify expressions. In this case, we need to handle the exponent before any multiplication or addition.
Step-by-Step Simplification
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Distribute the exponent: The exponent applies to both the coefficient (3) and the variable (a^2).
- (3a^2)^2 = 3^2 * (a^2)^2
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Simplify the coefficient: 3^2 = 9
- 9 * (a^2)^2
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Simplify the variable: When raising a power to another power, we multiply the exponents.
- 9 * a^(2*2) = 9 * a^4
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Combine the terms: 9a^4
Final Result
Therefore, the simplified form of (3a^2)^2 is 9a^4.
Key Takeaways
- Remember to distribute the exponent to all factors inside the parentheses.
- Apply the rules of exponents when simplifying powers of powers.
- Always follow the order of operations to ensure accurate simplification.