(3x^3y^2)(2y^3)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (3x^3y^2)(2y^3)

In mathematics, simplifying expressions often involves combining like terms and applying the rules of exponents. Let's break down how to simplify the expression (3x^3y^2)(2y^3).

Understanding the Rules of Exponents

The key to simplifying this expression lies in understanding the rules of exponents:

• Multiplication: When multiplying exponents with the same base, you add the powers. For example, x^m * x^n = x^(m+n).
• Commutative Property: The order of multiplication doesn't matter. For example, a * b = b * a.

Simplifying the Expression

1. Rearrange the terms: (3x^3y^2)(2y^3) = 3 * 2 * x^3 * y^2 * y^3

2. Combine the numerical coefficients: 3 * 2 * x^3 * y^2 * y^3 = 6 * x^3 * y^2 * y^3

3. Apply the multiplication rule for exponents: 6 * x^3 * y^2 * y^3 = 6x^3y^(2+3)

4. Simplify the exponents: 6x^3y^(2+3) = 6x^3y^5

Conclusion

Therefore, the simplified form of the expression (3x^3y^2)(2y^3) is 6x^3y^5.