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Simplifying the Expression (3m²n)³/mn⁴
This article will guide you through the steps of simplifying the algebraic expression (3m²n)³/mn⁴.
Understanding the Rules
To simplify this expression, we'll use the following rules of exponents:
- Power of a product: (ab)ⁿ = aⁿbⁿ
- Power of a power: (aⁿ)ᵐ = aⁿᵐ
- Division of exponents with the same base: aⁿ/aᵐ = aⁿ⁻ᵐ
Step-by-Step Solution
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Apply the power of a product rule: (3m²n)³ = 3³(m²)³(n)³ = 27m⁶n³
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Rewrite the expression: The original expression now becomes: (27m⁶n³)/(mn⁴)
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Apply the division of exponents rule: 27m⁶n³/mn⁴ = 27m⁶⁻¹n³⁻⁴ = 27m⁵n⁻¹
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Simplify negative exponents: We know that a⁻ⁿ = 1/aⁿ. Therefore: 27m⁵n⁻¹ = 27m⁵/n
Final Answer
The simplified form of the expression (3m²n)³/mn⁴ is 27m⁵/n.