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Simplifying (5x²y⁴)³
This article will guide you through the process of simplifying the expression (5x²y⁴)³.
Understanding the Power of a Product Rule
The fundamental rule we'll use here is the power of a product rule: (ab)ⁿ = aⁿbⁿ
This rule states that raising a product to a power is the same as raising each factor to that power.
Applying the Rule to Our Expression
Let's apply this rule to our expression (5x²y⁴)³:
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Apply the rule to each factor: (5x²y⁴)³ = 5³(x²)³(y⁴)³
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Simplify the exponents: 5³(x²)³(y⁴)³ = 125x⁶y¹²
Final Result
Therefore, the simplified form of (5x²y⁴)³ is 125x⁶y¹².