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Question

# Simplify by first writing in radical form.$9^{-5 / 2}$

Solution

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We need to simplify the given expression using radicals. To do so, we need to first express it in radicals. Using the rule of exponents, we will have

\begin{align*} &\quad\frac{1}{9^\frac{5}{2}} &&\text{Apply a^{-m/n} = \dfrac{1}{a^{m/n}}}\\ &= \frac{1}{\sqrt{9^{5}}} &&\text{Apply a^{m/n} = \sqrt[n]{a^m}}\\ &= \frac{1}{\sqrt{59049}} \end{align*}

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