Question

1. write the expression in radical form.

$x^{\frac{3}{5}}$

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 \(n>0\), \(n\in\mathbb{Z}\), \(m\in\mathbb{Z}\)). In the given expression \(x^{\frac{3}{5}}\), we can identify that \(a = x\), \(m = 3\) and \(n=5\).

Step2: Apply the rule

Using the rule \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\), substitute \(a = x\), \(m = 3\) and \(n = 5\) into the formula. So \(x^{\frac{3}{5}}=\sqrt[5]{x^{3}}\).

Answer:

\(\sqrt[5]{x^{3}}\)