%5E4.jpeg "(3m^2n)^4")
Simplifying Exponential Expressions: (3m²n)⁴
This article explores how to simplify the expression (3m²n)⁴. We'll break down the process step-by-step, highlighting the key concepts involved.
Understanding the Rules of Exponents
The expression involves exponents, which are a way of representing repeated multiplication. Here are the relevant rules for this problem:
- Product of powers: (aᵐ)ⁿ = aᵐⁿ
- Power of a product: (ab)ⁿ = aⁿbⁿ
Applying the Rules to Simplify
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Apply the power of a product rule: (3m²n)⁴ = 3⁴(m²)⁴(n)⁴
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Simplify each term:
- 3⁴ = 81
- (m²)⁴ = m⁸ (using the product of powers rule)
- n⁴ = n⁴
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Combine the terms: 81m⁸n⁴
Final Answer
Therefore, the simplified form of (3m²n)⁴ is 81m⁸n⁴.
Conclusion
Simplifying exponential expressions involves understanding the rules of exponents and applying them systematically. By breaking down the expression into smaller parts and using the appropriate rules, we can arrive at a simplified form.