[tex]~\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} \\\\ \sqrt[4]{\cfrac{k^{16}}{16z^4}}\implies \sqrt[4]{\cfrac{k^{4\cdot 4}}{2^4z^4}}\implies \sqrt[4]{\left( \cfrac{k^4}{2z} \right)^4}\implies \cfrac{k^4}{2z} \\\\[-0.35em] ~\dotfill[/tex][tex]\sqrt[8]{\cfrac{n^{18}p^7}{n^2p^{-1}}}\implies \sqrt[8]{\cfrac{n^{18}n^{-2}p^7p^1}{1}}\implies \sqrt[8]{n^{18-2}p^{7+1}} \\\\\\ \sqrt[8]{n^{16}p^8}\implies \sqrt[8]{(n^2)^8p^8}\implies n^2p~~ \begin{cases} n\ne 0\\ p \ne 0 \end{cases} \begin{array}{llll} \textit{why? because these values}\\ \textit{make an \underline{original} fraction}\\ \underline{unde fined} \end{array}[/tex]
