[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}[/tex]
[tex]\bf \cfrac{-20t^5u^2v^3}{48t^7u^4v}\implies \cfrac{-20}{48}\cdot \cfrac{t^5u^2v^3}{t^7u^4v^1}\implies \cfrac{-5}{12}\cdot \cfrac{v^3v^{-1}}{t^7t^{-5}u^4u^{-2}}\implies \cfrac{-5}{12}\cdot \cfrac{v^{3-1}}{t^{7-5}u^{4-2}} \\\\\\ \cfrac{-5}{12}\cdot \cfrac{v^2}{t^2u^2}\implies \cfrac{-5v^2}{12t^2 u^2}[/tex]
