[tex]\bf ~\hspace{7em}\textit{negative exponents}
\\\\
a^{-n} \implies \cfrac{1}{a^n}
~\hspace{4.5em}
a^n\implies \cfrac{1}{a^{-n}}
~\hspace{4.5em}
\cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
32^{-\frac{2}{5}}~~
\begin{cases}
32=2\cdot 2\cdot 2\cdot 2\cdot 2\\
\qquad 2^5
\end{cases}\implies (2^5)^{-\frac{2}{5}}\implies 2^{-\frac{2}{5}\cdot 5}\implies 2^{-2}
\\\\\\
\cfrac{1}{2^2}\implies \cfrac{1}{4}[/tex]
