%5E3.jpeg "(5x^2y^4)^3")
Simplifying (5x²y⁴)³
In this article, we will explore how to simplify the expression (5x²y⁴)³.
Understanding the Concept
The expression involves exponents and parentheses. Here's how to break it down:
- Parentheses: The parentheses indicate that we need to apply the exponent to the entire expression inside.
- Exponent: The exponent '3' tells us to multiply the base (the expression inside the parentheses) by itself three times.
Applying the Rules
To simplify, we use the following rules:
- Power of a Product Rule: (ab)ⁿ = aⁿbⁿ
- Power of a Power Rule: (aⁿ)ᵐ = aⁿᵐ
Step-by-Step Simplification
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Apply the Power of a Product Rule: (5x²y⁴)³ = 5³ (x²)³ (y⁴)³
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Apply the Power of a Power Rule: 5³ (x²)³ (y⁴)³ = 125x⁶y¹²
Final Answer
Therefore, the simplified form of (5x²y⁴)³ is 125x⁶y¹².
Conclusion
This example demonstrates how to effectively simplify expressions with exponents and parentheses. By applying the appropriate rules, we can arrive at a simplified and more manageable form.