(4x^2y^3)^4

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions with Exponents: (4x^2y^3)^4

This article will guide you through simplifying the expression (4x^2y^3)^4.

Understanding the Rules

Before we begin, let's review some key exponent rules:

• Product of powers: (x^m)^n = x^(m*n)
• Power of a product: (xy)^n = x^n * y^n

Simplifying the Expression

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

2. Apply the product of powers rule: 4^4 * (x^2)^4 * (y^3)^4 = 256 * x^(24) * y^(34)

3. Simplify the exponents: 256 * x^(24) * y^(34) = 256x^8y^12

Conclusion

Therefore, the simplified form of (4x^2y^3)^4 is 256x^8y^12. By understanding and applying the exponent rules, we can efficiently simplify complex expressions.