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(4x^5y)^3

2 min read Jun 16, 2024
(4x^5y)^3

Simplifying (4x^5y)^3

In mathematics, simplifying expressions is a fundamental skill. One common type of expression involves raising a monomial to a power. Let's explore how to simplify the expression (4x^5y)^3.

Understanding the Rules

To simplify this expression, we need to recall the following rules of exponents:

  • Power of a product: (ab)^n = a^n * b^n
  • Power of a power: (a^m)^n = a^(m*n)

Applying the Rules

  1. Apply the power of a product rule: (4x^5y)^3 = 4^3 * (x^5)^3 * y^3

  2. Apply the power of a power rule: 4^3 * (x^5)^3 * y^3 = 64 * x^(5*3) * y^3

  3. Simplify: 64 * x^(5*3) * y^3 = 64x^15y^3

Conclusion

Therefore, the simplified form of (4x^5y)^3 is 64x^15y^3. By understanding the rules of exponents and applying them systematically, we can effectively simplify complex expressions.

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