Select the equivalent expression.
\[
\left(\frac{d^{6}}{d^{-7}}\right)^{\frac{4}{39}}
\]
\( \frac{1}{\sqrt[4]{d^{3}}} \)
\( \sqrt[3]{d^{4}} \)
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\( \frac{1}{\sqrt[3]{d^{4}}} \)
\( \sqrt[4]{d^{3}} \)

Answer

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Answer

\(= d^{\frac{52}{39}}\)

Steps

Step 1 ：\(\left(\frac{d^{6}}{d^{-7}}\right)^{\frac{4}{39}} = \left(d^{(6 + 7)}\right)^{\frac{4}{39}}\)

Step 2 ：\(= \left(d^{13}\right)^{\frac{4}{39}}\)

Step 3 ：\(= d^{\frac{52}{39}}\)