[tex]\bf ~~~~~~~~~~~~\textit{negative exponents}
\\\\
a^{-n} \implies \cfrac{1}{a^n}
\qquad \qquad
\cfrac{1}{a^n}\implies a^{-n}
\qquad \qquad
a^n\implies \cfrac{1}{a^{-n}}
\\\\
-------------------------------[/tex]
[tex]\bf \cfrac{2x^{-\frac{7}{4}}}{4x^{\frac{4}{3}}}\implies \cfrac{2}{4}\cdot \cfrac{x^{-\frac{7}{4}}}{x^{\frac{4}{3}}}\implies \cfrac{1}{2}\cdot \cfrac{1}{x^{\frac{4}{3}}\cdot x^{\frac{7}{4}}}\implies \cfrac{1}{2}\cdot \cfrac{1}{x^{\frac{4}{3}+\frac{7}{4}}}\implies \cfrac{1}{2}\cdot \cfrac{1}{x^{\frac{16+21}{12}}}
\\\\\\
\cfrac{1}{2}\cdot \cfrac{1}{x^{\frac{37}{12}}}\implies \cfrac{1}{2x^{\frac{37}{12}}}[/tex]
