Problem

Select the equivalent expression.
\[
\sqrt[14]{\frac{z}{z^{5}}}
\]
\( z^{\frac{7}{2}} \)
\( z^{-\frac{7}{2}} \)
Submit Answer
\( z^{-\frac{2}{7}} \)
\( z^{\frac{2}{7}} \)

Answer

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Hide Steps

Answer

\(z^{-\frac{4}{14}} = z^{-\frac{2}{7}}\)

Steps

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 ：\(z^{-\frac{4}{14}} = z^{-\frac{2}{7}}\)

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