(25x^4y^6)^1/2

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions with Fractional Exponents: (25x^4y^6)^1/2

Fractional exponents represent roots. A fractional exponent of 1/2 signifies taking the square root of the base. Let's simplify the expression (25x^4y^6)^1/2:

Understanding the Properties

We'll use these key properties of exponents:

• (ab)^n = a^n * b^n: The power of a product is the product of the powers.
• (a^m)^n = a^(m*n): The power of a power is the base raised to the product of the exponents.

Step-by-Step Simplification

1. Apply the first property: (25x^4y^6)^1/2 = 25^(1/2) * x^(4 * 1/2) * y^(6 * 1/2)

2. Simplify: 25^(1/2) * x^(4 * 1/2) * y^(6 * 1/2) = 5 * x^2 * y^3

Final Result

Therefore, (25x^4y^6)^1/2 simplifies to 5x^2y^3.