Select the equivalent expression.
\[
\sqrt[4]{\frac{z^{-5}}{z^{-4}}}
\]
\( z^{4} \)
\( z^{-\frac{1}{4}} \)
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\( z^{-4} \)
\( z^{\frac{1}{4}} \)

Answer

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Answer

Apply the fourth root: \( z^{-\frac{1}{4}} \)

Steps

Step 1 ：Simplify the expression inside the fourth root: \( \frac{z^{-5}}{z^{-4}} \)

Step 2 ：Rewrite as a single exponent: \( z^{-5 - (-4)} \)

Step 3 ：Simplify the exponent: \( z^{-1} \)

Step 4 ：Apply the fourth root: \( z^{-\frac{1}{4}} \)