[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}\\\\ \cfrac{-27m^3 n^{-1}}{9m^2 n}\div \cfrac{(3mn)^{-2}}{(2mn)^2}\implies \cfrac{-27m^3}{9 m^2 n n^1}\div \cfrac{1}{(2mn)^2(3mn)^{2}}[/tex]
[tex]\bf \cfrac{-27m^3 m^{-2}}{9 n n^1}\div \cfrac{1}{(2mn\cdot 3mn)^{2}}\implies \cfrac{-27m^{3-2}}{9n^{1+1}}\div \cfrac{1}{(6m^{1+1}n^{1+1})^2} \\\\\\ \cfrac{-27m}{9n^2}\div \cfrac{1}{(6m^2n^2)^2}\implies \cfrac{-3^3 m}{3^2n^2}\div \cfrac{1}{6^2m^4n^4}\implies \cfrac{-3m}{n^2}\div \cfrac{1}{36m^4n^4} \\\\\\ \cfrac{-3m}{n^2}\cdot \cfrac{36m^4n^4}{1}\implies \cfrac{-108 m m^4n^4n^{-2}}{1}\implies -108m^5n^2[/tex]
