[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{(2a^7b)^2}{32b^6}\implies \cfrac{(2^2a^{7\cdot 2}b^2)}{32b^6}\implies \cfrac{4a^{14}b^2}{32b^6}\implies \cfrac{a^{14}}{8b^6b^{-2}}\implies \cfrac{a^{14}}{8b^{6-2}}\implies \cfrac{a^{14}}{8b^4}[/tex]
