Question

How do you solve this?

Answer 1

$\bf ~~~~~~~~~~~~\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^{-n} \qquad \qquad a^n\implies \cfrac{1}{a^{-n}} \\\\ -------------------------------$

$\bf \cfrac{2x^{-\frac{7}{4}}}{4x^{\frac{4}{3}}}\implies \cfrac{2}{4}\cdot \cfrac{x^{-\frac{7}{4}}}{x^{\frac{4}{3}}}\implies \cfrac{1}{2}\cdot \cfrac{1}{x^{\frac{4}{3}}\cdot x^{\frac{7}{4}}}\implies \cfrac{1}{2}\cdot \cfrac{1}{x^{\frac{4}{3}+\frac{7}{4}}}\implies \cfrac{1}{2}\cdot \cfrac{1}{x^{\frac{16+21}{12}}} \\\\\\ \cfrac{1}{2}\cdot \cfrac{1}{x^{\frac{37}{12}}}\implies \cfrac{1}{2x^{\frac{37}{12}}}$