%5E1%2F2-in-radical-form.jpeg "(25x^2)^1/2 In Radical Form")
Simplifying (25x^2)^1/2 in Radical Form
The expression (25x^2)^1/2 represents the square root of 25x^2. We can simplify this expression by applying the properties of exponents and radicals.
Breaking down the expression
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Exponent Rule: (a^m)^n = a^(mn) Applying this rule, we can rewrite the expression as: 25^(1/2) * x^(2(1/2)).
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Radical Rule: a^(1/n) = n√a Using this rule, we get: √25 * x^(2/2).
Simplifying further
- Square Root: √25 = 5
- Exponent: x^(2/2) = x^1 = x
Final Solution
Combining the simplified terms, the expression (25x^2)^1/2 in radical form becomes 5x.