Question: Write the following as an exponential expression. \[ \sqrt[8]{a^5} \]

Write the following as an exponential expression. \[ \sqrt[8]{a^5} \]

Solution

To convert the given radical expression to an exponential expression, we start with: \[ \sqrt[8]{a^5} \] In exponential form, a radical expression \(\sqrt[n]{x^m}\) can be written as: \[ x^{m/n} \] Applying this rule to the problem: Substitute \(a^5\) for \(x^m\) and 8 for \(n\). \[ a^{5/8} \] So, the exponential expression is \(a^{5/8}\).