Problem
Select the equivalent expression. \[ \sqrt[14]{\frac{z}{z^{5}}} \] \( z^{\frac{7}{2}} \) \( z^{-\frac{7}{2}} \) Submit Answer \( z^{-\frac{2}{7}} \) \( z^{\frac{2}{7}} \)
Solution
Step 1 ：\(\sqrt[14]{\frac{z}{z^{5}}} = \sqrt[14]{z^{1-5}}\)
Step 2 ：\(\sqrt[14]{z^{-4}} = z^{-\frac{4}{14}}\)
Step 3 ：\(z^{-\frac{4}{14}} = z^{-\frac{2}{7}}\)
