Question

question
write the expression in radical form.
$x^{\frac{2}{5}}$

Explanation:

Step1: Recall the exponent - radical rule

The rule for converting a rational exponent to radical form is \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\) (where \(n\gt0\), \(n\in\mathbb{Z}\), \(m\in\mathbb{Z}\)). In the given expression \(x^{\frac{2}{5}}\), we have \(a = x\), \(m = 2\) and \(n=5\).

Step2: Apply the rule

Using the rule \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\), substitute \(a = x\), \(m = 2\) and \(n = 5\) into the formula. We get \(\sqrt[5]{x^{2}}\).

Answer:

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