[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] ~\dotfill\\\\ \cfrac{2^4\times 4^6}{2^{-3}\times 4^4}\implies 2^4\cdot 2^3\cdot 4^6\cdot 4^{-4}\implies 2^{4+3}\cdot 4^{6-4}\implies 2^7\cdot 4^2\implies 2^7\cdot (2^2)^2 \\\\\\ 2^7\cdot 2^{2\cdot 2}\implies 2^7\cdot 2^4\implies 2^{7+4}\implies 2^{11}\implies 2048[/tex]
