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(xy^4)^6

less than a minute read Jun 17, 2024
(xy^4)^6

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

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

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

  3. 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.

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