[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} \\\\\\ ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \cfrac{10}{10^{\frac{3}{4}}}\implies \cfrac{10^1}{10^{\frac{3}{4}}}\implies \cfrac{10^{\frac{4}{4}}}{10^{\frac{3}{4}}}\implies 10^{\frac{4}{4}}\cdot 10^{-\frac{3}{4}}\implies 10^{\frac{4}{4}-\frac{3}{4}}\implies 10^{\frac{1}{4}}\implies \sqrt[4]{10}[/tex]
