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(3x^3y)^2

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

Simplifying (3x^3y)^2

This article will explore how to simplify the expression (3x^3y)^2.

Understanding the Rules of Exponents

To simplify this expression, we need to understand the basic 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. Distribute the exponent: We can rewrite the expression as (3^2) * (x^3)^2 * (y)^2. This is based on the power of a product rule.

  2. Simplify the exponents:

    • 3^2 = 9
    • (x^3)^2 = x^(3*2) = x^6 (using the power of a power rule)
    • y^2 = y^2

  3. Combine the terms: The simplified expression is 9x^6y^2.

Conclusion

Therefore, the simplified form of (3x^3y)^2 is 9x^6y^2. By understanding the basic rules of exponents, we can easily simplify expressions involving powers.

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