Question

Can someone help me with these questions? I am getting really frustrated.

Answer 1

`~\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`
`\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\\e 0\\ p \\e 0 \end{cases} \begin{array}{llll} \textit{why? because these values}\\ \textit{make an \underline{original} fraction}\\ \underline{unde fined} \end{array}`