Simplifying (xy^4)^6
This expression involves a combination of exponents and the power of a product rule. Let's break down how to simplify it:
Understanding the Rules
 Power of a Product Rule: (ab)^n = a^n * b^n
 Power of a Power Rule: (a^m)^n = a^(m*n)
Applying the Rules

Apply the Power of a Product Rule: (xy^4)^6 = x^6 * (y^4)^6

Apply the Power of a Power Rule: x^6 * (y^4)^6 = x^6 * y^(4*6)

Simplify: x^6 * y^(4*6) = x^6 * y^24
Conclusion
Therefore, the simplified form of (xy^4)^6 is x^6 * y^24. This process demonstrates how understanding exponent rules allows us to simplify complex expressions efficiently.