%5E4.jpeg "(-6x^2y^4)^4")
Simplifying Expressions with Exponents: (-6x²y⁴)⁴
This article will guide you through the process of simplifying the expression (-6x²y⁴)⁴.
Understanding the Rules of Exponents
Before we start, let's recall the essential rules of exponents:
- Product of Powers: (a^m) * (a^n) = a^(m+n)
- Power of a Product: (ab)^n = a^n * b^n
- Power of a Power: (a^m)^n = a^(m*n)
Step-by-Step Simplification
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Apply the Power of a Product Rule: (-6x²y⁴)⁴ = (-6)⁴ * (x²)⁴ * (y⁴)⁴
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Apply the Power of a Power Rule: (-6)⁴ * (x²)⁴ * (y⁴)⁴ = 1296 * x⁸ * y¹⁶
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Combine the terms: 1296 * x⁸ * y¹⁶ = 1296x⁸y¹⁶
Final Answer
Therefore, the simplified expression of (-6x²y⁴)⁴ is 1296x⁸y¹⁶.