Question

rewrite ((ch)^{\frac{2}{3}}) in radical form. simplify in needed.

Explanation:

Step1: Recall the exponent to radical rule

The rule for converting an exponent of the form \(a^{\frac{m}{n}}\) to radical form is \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\) (or equivalently \((\sqrt[n]{a})^{m}\)).

Step2: Apply the rule to \((ch)^{\frac{2}{3}}\)

Here, \(a = ch\), \(m = 2\), and \(n=3\). Using the rule \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\), we substitute the values to get \(\sqrt[3]{(ch)^{2}}\). We can also expand \((ch)^{2}\) as \(c^{2}h^{2}\), so it can be written as \(\sqrt[3]{c^{2}h^{2}}\).

Answer:

\(\sqrt[3]{(ch)^{2}}\) (or \(\sqrt[3]{c^{2}h^{2}}\))