(2x^2y^3)^3

Jasonbradley

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Jun 16, 2024

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Simplifying (2x²y³)^3

This article will guide you through the steps of simplifying the expression (2x²y³)^3.

Understanding the Properties

To simplify this expression, we'll utilize the following properties of exponents:

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

Step-by-Step Simplification

1. Apply the Power of a Product property:

   (2x²y³)^3 = 2³ * (x²)^3 * (y³)^3

2. Apply the Power of a Power property:

   2³ * (x²)^3 * (y³)^3 = 8 * x^(23) * y^(33)

3. Simplify:

   8 * x^(23) * y^(33) = 8x⁶y⁹

Conclusion

Therefore, the simplified form of (2x²y³)^3 is 8x⁶y⁹. This process highlights how understanding the fundamental properties of exponents allows us to efficiently simplify complex expressions.