Question

express $27^{\frac{1}{3}}$ in simplest radical form.

Explanation:

Step1: Recall the exponent rule

The exponent rule states that \(a^{\frac{m}{n}}=\sqrt[n]{a^m}\), where \(a\) is a real number, \(m\) and \(n\) are integers with \(n>0\). For \(27^{\frac{1}{3}}\), we have \(m = 1\) and \(n=3\), so \(27^{\frac{1}{3}}=\sqrt[3]{27^1}=\sqrt[3]{27}\).

Step2: Find the cube root of 27

We know that \(3\times3\times3 = 3^3=27\), so \(\sqrt[3]{27}=\sqrt[3]{3^3}\). And by the property of cube roots, \(\sqrt[3]{x^3}=x\) for any real number \(x\). So \(\sqrt[3]{3^3} = 3\).

Answer:

\(3\)