Problem
Select the equivalent expression. \[ \sqrt[6]{v^{2} \cdot v^{7}} \] \( v^{-\frac{3}{2}} \) \( v^{-\frac{2}{3}} \) Submit Answer \( v^{\frac{2}{3}} \) \( v^{\frac{3}{2}} \)
Solution
Step 1 ：\( \sqrt[6]{v^{2} \cdot v^{7}} = \sqrt[6]{v^{2 + 7}} \)
Step 2 ：\( \sqrt[6]{v^{9}} = v^{\frac{9}{6}} \)
Step 3 ：\( v^{\frac{9}{6}} = v^{\frac{3}{2}} \)
