(3m^2n)^3/mn^4

Jasonbradley

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Jun 16, 2024

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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

1. Apply the power of a product rule: (3m²n)³ = 3³(m²)³(n)³ = 27m⁶n³

2. Rewrite the expression: The original expression now becomes: (27m⁶n³)/(mn⁴)

3. Apply the division of exponents rule: 27m⁶n³/mn⁴ = 27m⁶⁻¹n³⁻⁴ = 27m⁵n⁻¹

4. 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.