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Simplifying Expressions with Exponents: (3x^2)^3
This article explores the simplification of the expression (3x^2)^3. We'll break down the process step-by-step to understand how to handle exponents within parentheses.
Understanding the Rules
Before diving into the calculation, let's recap the key rules of exponents:
- Product of powers: When multiplying powers with the same base, add the exponents. For example, x^m * x^n = x^(m+n).
- Power of a power: When raising a power to another power, multiply the exponents. For example, (x^m)^n = x^(m*n).
- Power of a product: When raising a product to a power, apply the power to each factor. For example, (xy)^n = x^n * y^n.
Simplifying the Expression
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Apply the power of a power rule: We have (3x^2)^3, which means we raise each factor within the parentheses to the power of 3.
- 3^3 = 27
- (x^2)^3 = x^(2*3) = x^6
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Combine the results: Now we have 27 * x^6.
The Final Result
Therefore, the simplified expression for (3x^2)^3 is 27x^6.
Key Takeaways
Remember these rules when dealing with exponents:
- Power of a power: Multiply the exponents.
- Power of a product: Apply the power to each factor.
By understanding these rules, you can confidently simplify expressions involving exponents and parentheses.