(2x^2y^3)^2

Jasonbradley

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Jun 16, 2024

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

In mathematics, simplifying expressions is a fundamental skill. One common type of expression involves raising a product of variables and constants to a power. This article will guide you through simplifying the expression (2x^2y^3)^2.

Understanding the Rules of Exponents

To simplify this expression, we need to understand the rules of exponents. Here are the relevant rules:

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

Applying the Rules to Simplify

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

2. Apply the Power of a power rule: 2^2 * (x^2)^2 * (y^3)^2 = 4 * x^(22) * y^(32)

3. Simplify the exponents: 4 * x^(22) * y^(32) = 4x^4y^6

Final Result

Therefore, the simplified form of (2x^2y^3)^2 is 4x^4y^6.