%5E3.jpeg "(3ab^2)^3")
Simplifying (3ab^2)^3
In mathematics, simplifying expressions is crucial for understanding their value and relationships. One such expression we'll explore today is (3ab^2)^3.
Understanding the Rules
To simplify this expression, we need to understand a couple of key rules:
- Power of a product: (ab)^n = a^n * b^n. This rule states that raising a product to a power is the same as raising each factor to that power.
- Power of a power: (a^m)^n = a^(m*n). This rule states that raising a power to another power is the same as multiplying the exponents.
Applying the Rules
Let's break down the simplification process step by step:
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Apply the power of a product rule: (3ab^2)^3 = 3^3 * a^3 * (b^2)^3
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Apply the power of a power rule: 3^3 * a^3 * (b^2)^3 = 3^3 * a^3 * b^(2*3)
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Simplify the exponents: 3^3 * a^3 * b^(2*3) = 27a^3b^6
The Simplified Expression
Therefore, the simplified form of (3ab^2)^3 is 27a^3b^6.
Key takeaways:
- By understanding and applying the rules of exponents, we can simplify complex expressions.
- Simplifying expressions often makes them easier to work with and understand.
- The steps involved in simplifying expressions are often clear and logical, making the process relatively straightforward.