%5E2-simplify.jpeg "(5x^3)^2 Simplify")
Simplifying (5x^3)^2
In mathematics, simplifying expressions is a crucial skill. One common type of simplification involves exponents. Let's break down how to simplify the expression (5x^3)^2.
Understanding the Rules
The key principle here is the power of a product rule:
(ab)^n = a^n * b^n
This rule states that when raising a product to a power, we can distribute the power to each factor within the product.
Applying the Rule
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Identify the factors: In our expression, (5x^3)^2, the factors are 5 and x^3.
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Apply the power of a product rule: (5x^3)^2 = 5^2 * (x^3)^2
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Simplify the powers: 5^2 = 25 (x^3)^2 = x^(3*2) = x^6
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Combine the simplified terms: 25 * x^6 = 25x^6
The Result
Therefore, the simplified form of (5x^3)^2 is 25x^6.
Key Takeaways
- Remember the power of a product rule and its application.
- Break down complex expressions into smaller, manageable parts.
- Always simplify powers by multiplying exponents when needed.