(2x^3y^2)^3

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (2x³y²)^3

This article explores the simplification of the expression (2x³y²)^3. We'll delve into the process and the underlying mathematical concepts involved.

Understanding Exponents

Before we tackle the simplification, let's recap the fundamentals of exponents:

• Exponent: An exponent indicates how many times a base number is multiplied by itself. For instance, in the expression x², the base is 'x', and the exponent is '2', meaning x is multiplied by itself twice (x * x).

• Power of a Power: When raising a power to another power, we multiply the exponents. For example, (x²)³ = x^(2*3) = x⁶.

• Power of a Product: When a product is raised to a power, we apply the power to each factor within the product. For example, (ab)² = a²b².

Simplifying (2x³y²)^3

Now, let's apply these concepts to simplify (2x³y²)^3:

1. Distribute the exponent: We apply the exponent '3' to each factor within the parentheses. (2x³y²)^3 = 2³ (x³)^3 (y²)^3

2. Simplify each term:

   • 2³ = 2 * 2 * 2 = 8
   • (x³)^3 = x^(3*3) = x⁹
   • (y²)^3 = y^(2*3) = y⁶

3. Combine the simplified terms: 8 * x⁹ * y⁶ = 8x⁹y⁶

Therefore, the simplified form of (2x³y²)^3 is 8x⁹y⁶.