Problem

Select the equivalent expression.
\[
\sqrt[6]{v^{2} \cdot v^{7}}
\]
\( v^{-\frac{3}{2}} \)
\( v^{-\frac{2}{3}} \)
Submit Answer
\( v^{\frac{2}{3}} \)
\( v^{\frac{3}{2}} \)

Answer

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Answer

\( v^{\frac{9}{6}} = v^{\frac{3}{2}} \)

Steps

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 ：\( v^{\frac{9}{6}} = v^{\frac{3}{2}} \)

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