1. **Problem:** Find the cube root of each of the following numbers: 0, 27, 729, 1728, 6859, and \(\left(\frac{1}{2}\right)^3\). 2. **Formula:** The cube root of a number \(a\) is a number \(b\) such that \(b^3 = a\). It is denoted as \(\sqrt[3]{a}\). 3. **Steps:** 1. \(\sqrt[3]{0} = 0\) because \(0^3 = 0\). 2. \(\sqrt[3]{27} = 3\) because \(3^3 = 27\). 3. \(\sqrt[3]{729} = 9\) because \(9^3 = 729\). 4. \(\sqrt[3]{1728} = 12\) because \(12^3 = 1728\). 5. \(\sqrt[3]{6859} = 19\) because \(19^3 = 6859\). 6. \(\sqrt[3]{\left(\frac{1}{2}\right)^3} = \frac{1}{2}\) because \(\left(\frac{1}{2}\right)^3 = \frac{1}{8}\) and cube root of \(\frac{1}{8}\) is \(\frac{1}{2}\). **Final answers:** \[ \sqrt[3]{0} = 0, \quad \sqrt[3]{27} = 3, \quad \sqrt[3]{729} = 9, \quad \sqrt[3]{1728} = 12, \quad \sqrt[3]{6859} = 19, \quad \sqrt[3]{\left(\frac{1}{2}\right)^3} = \frac{1}{2} \]