Problem
Select the equivalent expression. \[ \left(\frac{1}{s^{-1} \cdot s^{8}}\right)^{\frac{3}{14}} \] \( \sqrt{s^{3}} \) \( \frac{1}{\sqrt[3]{s^{2}}} \) Submit Answer \( \sqrt[3]{s^{2}} \) \( \frac{1}{\sqrt{s^{3}}} \)
Solution
Step 1 ：\( \left(\frac{1}{s^{-1} \cdot s^{8}}\right)^{\frac{3}{14}} = \left(\frac{1}{s^{7}}\right)^{\frac{3}{14}} \)
Step 2 ：\( = \frac{1}{s^{\frac{7}{14} \cdot 3}} \)
Step 3 ：\( = \frac{1}{s^{\frac{3}{2}}} \)
