Problem

Select the equivalent expression.
\[
\sqrt[8]{\frac{d^{-8}}{d^{-6}}}
\]
\( d^{-4} \)
\( d^{4} \)
Submit Answer
\( d^{\frac{1}{4}} \)
\( d^{-\frac{1}{4}} \)

Answer

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Answer

\( d^{-\frac{1}{4}} \)

Steps

Step 1 ：\sqrt[8]{\frac{d^{-8}}{d^{-6}}} = \sqrt[8]{d^{-8} \cdot d^{6}}

Step 2 ：\sqrt[8]{d^{-8+6}} = \sqrt[8]{d^{-2}}

Step 3 ：\( d^{-\frac{1}{4}} \)

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