Question

question
write the expression in radical form.
$x^{\frac{5}{2}}$
answer attempt 1 out of 2
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Explanation:

Step1: Recall the exponent - radical relationship

The formula for converting a rational exponent to radical form is \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\) (where \(n>0\), \(n\in\mathbb{Z}\), \(m\in\mathbb{Z}\)). For the expression \(x^{\frac{5}{2}}\), we have \(a = x\), \(m = 5\), and \(n=2\).

Step2: Apply the formula

Using the formula \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\), substitute \(a = x\), \(m = 5\), and \(n = 2\) into it. We get \(\sqrt[2]{x^{5}}\), and since the index of a square root (when \(n = 2\)) is usually not written explicitly, we can also write it as \(\sqrt{x^{5}}\).

Answer:

\(\sqrt{x^{5}}\) (or \(\sqrt[2]{x^{5}}\))