Problem
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 \( x^{4} \) \( \frac{1}{x^{4}} \)
Solution
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 ：\( = x^{\frac{13}{52}} \)
