Select the equivalent expression.
\[
\left(\frac{1}{x^{-6} \cdot x^{-7}}\right)^{\frac{1}{52}}
\]
\( \sqrt[4]{x} \)
\( \frac{1}{\sqrt[4]{x}} \)
Submit Answer
\( x^{4} \)
\( \frac{1}{x^{4}} \)

Answer

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Answer

\( = x^{\frac{13}{52}} \)

Steps

Step 1 ：\( \left(\frac{1}{x^{-6} \cdot x^{-7}}\right)^{\frac{1}{52}} = \left(x^{6} \cdot x^{7}\right)^{\frac{1}{52}} \)

Step 2 ：\( = \left(x^{6+7}\right)^{\frac{1}{52}} = \left(x^{13}\right)^{\frac{1}{52}} \)

Step 3 ：\( = x^{\frac{13}{52}} \)