[tex]\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\
a^{-{ n}} \implies \cfrac{1}{a^{ n}}
\qquad \qquad
\cfrac{1}{a^{ n}}\implies a^{-{ n}}
\qquad \qquad
a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}
\\\\
-------------------------------\\\\
[/tex]
[tex]\bf 3^{5x-9}=\left( \cfrac{1}{27} \right)^{2x-8}\qquad \boxed{27=3^3}\qquad 3^{5x-9}=\left( \cfrac{1}{3^3} \right)^{2x-8}
\\\\\\
3^{5x-9}=\left( 3^{-3} \right)^{2x-8}\implies 3^{5x-9}= 3^{-3(2x-8)}
\\\\\\
3^{5x-9}= 3^{-6x+24}\impliedby
\begin{array}{llll}
\textit{the bases are the same, then}\\
\textit{the exponents must be the same}
\end{array}
\\\\\\
5x-9=-6x+24\implies 11x=33\implies x=\cfrac{33}{11}\implies x=3[/tex]
