[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{a^3b^{-4}}{a^2b^3a^{-5}}\implies \cfrac{a^3}{1}\cdot b^{-4}\cdot \cfrac{1}{a^2}\cdot \cfrac{1}{b^3}\cdot \cfrac{1}{a^{-5}}\implies a^3\cdot b^{-4}\cdot a^{-2}\cdot b^{-3}\cdot a^5 \\\\\\ a^3a^5a^{-2}b^{-4}b^{-3}\implies a^{3+5-2}b^{-4-3}\implies a^6b^{-7}[/tex]
