(5xy^2)^4

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions with Exponents: (5xy^2)^4

In mathematics, understanding how to simplify expressions with exponents is crucial. One common example involves expressions like (5xy^2)^4. Let's break down the steps to simplify this expression:

Understanding the Rules

• Power of a product: When a product is raised to a power, each factor is raised to that power. This means: (ab)^n = a^n * b^n.
• Power of a power: When a power is raised to another power, the exponents are multiplied. This means: (a^m)^n = a^(m*n).

Applying the Rules to (5xy^2)^4

1. Apply the power of a product rule:

   • (5xy^2)^4 = 5^4 * x^4 * (y^2)^4

2. Apply the power of a power rule:

   • 5^4 * x^4 * (y^2)^4 = 5^4 * x^4 * y^(2*4)

3. Simplify the exponents:

   • 5^4 * x^4 * y^(2*4) = 625 * x^4 * y^8

Conclusion

Therefore, the simplified form of (5xy^2)^4 is 625x^4y^8.

This process demonstrates how applying the fundamental rules of exponents allows us to simplify complex expressions, making them easier to understand and work with.