Question

write the following as an exponential expression.
\sqrt4{11^3}

Explanation:

Step1: Recall the radical to exponent rule

The \(n\)-th root of a number \(a^m\) can be written as \(a^{\frac{m}{n}}\). Here, we have the 4th root of \(11^3\), so \(n = 4\) and \(m = 3\), and the base \(a = 11\).

Step2: Apply the rule

Using the rule \(\sqrt[n]{a^m}=a^{\frac{m}{n}}\), substitute \(n = 4\), \(m = 3\), and \(a = 11\) into the formula. We get \(11^{\frac{3}{4}}\).

Answer:

\(11^{\frac{3}{4}}\)