Select the equivalent expression.
\[
\sqrt[18]{\frac{b^{-1}}{b^{8}}}
\]
\( b^{2} \)
\( b^{-2} \)
Submit Answer
\( b^{\frac{1}{2}} \)
\( b^{-\frac{1}{2}} \)

Answer

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Answer

\(\sqrt[18]{b^{-9}} = b^{\frac{-9}{18}} = b^{-\frac{1}{2}}\)

Steps

Step 1 ：\(\sqrt[18]{\frac{b^{-1}}{b^{8}}} = \sqrt[18]{b^{-1-8}}\)

Step 2 ：\(\sqrt[18]{b^{-1-8}} = \sqrt[18]{b^{-9}}\)

Step 3 ：\(\sqrt[18]{b^{-9}} = b^{\frac{-9}{18}} = b^{-\frac{1}{2}}\)