Question

write the expression in exponential form.
\sqrt2{x^{3}}

Explanation:

Step1: Recall the radical to exponential rule

The \(n\)-th root of a number \(a\) can be written as \(a^{\frac{1}{n}}\), and \(\sqrt[n]{a^m}=a^{\frac{m}{n}}\). Here, the radical is a square root, so \(n = 2\), and the expression inside the radical is \(x^3\), so \(m=3\).

Step2: Apply the rule to the given expression

For \(\sqrt[2]{x^3}\) (since square root is 2nd root), using the formula \(\sqrt[n]{a^m}=a^{\frac{m}{n}}\), we substitute \(n = 2\) and \(m = 3\) and \(a=x\). So we get \(x^{\frac{3}{2}}\).

Answer:

\(x^{\frac{3}{2}}\)