Simplifying (4xy⁴)³
This expression involves the concept of exponents and their properties, specifically the power of a product rule and the power of a power rule. Let's break down how to simplify it stepbystep:
Understanding the Rules
 Power of a product rule: (ab)ⁿ = aⁿbⁿ
 Power of a power rule: (aⁿ)ᵐ = aⁿᵐ
Applying the Rules

Apply the power of a product rule: (4xy⁴)³ = 4³ (x)³ (y⁴)³

Apply the power of a power rule: 4³ (x)³ (y⁴)³ = 64x³y¹²
Final Answer
Therefore, the simplified form of (4xy⁴)³ is 64x³y¹².