(25x^4)^1/2

Jasonbradley

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Jun 16, 2024

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Simplifying (25x^4)^(1/2)

This expression represents the square root of 25x^4. Here's how to simplify it:

Understanding the Properties

• Square Roots: The square root of a number is a value that, when multiplied by itself, equals the original number. For example, the square root of 9 is 3 because 3 * 3 = 9.
• Exponents: An exponent indicates how many times a base number is multiplied by itself. For example, x^4 means x * x * x * x.
• Fractional Exponents: A fractional exponent represents a root. The denominator of the fraction indicates the type of root. For example, x^(1/2) is the square root of x.

Simplifying the Expression

1. Separate the terms: (25x^4)^(1/2) = (25)^(1/2) * (x^4)^(1/2)
2. Calculate the square root of 25: (25)^(1/2) = 5
3. Apply the power rule for exponents: (x^4)^(1/2) = x^(4 * 1/2) = x^2
4. Combine the simplified terms: 5 * x^2 = 5x^2

Therefore, the simplified form of (25x^4)^(1/2) is 5x^2.