[tex]\bf \left.\qquad \qquad \right.\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}}}}
\\\\\\ and\qquad a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\
-------------------------------\\\\[/tex]
[tex]\fb 3x^{-\frac{4}{3}}+6x^{\frac{1}{3}}\implies 3\cdot \cfrac{1}{x^{\frac{4}{3}}}+6x^{\frac{1}{3}}\implies \cfrac{3}{x^{\frac{4}{3}}}+6x^{\frac{1}{3}}\impliedby LCD=x^{\frac{4}{3}}
\\\\\\
\cfrac{3+(6x^{\frac{1}{3}})(x^{\frac{4}{3}})}{x^{\frac{4}{3}}}\implies
\cfrac{3+6x^{\frac{1}{3}+\frac{4}{3}}}{x^{\frac{4}{3}}}\implies
\cfrac{3+6x^{\frac{5}{3}}}{x^{\frac{4}{3}}}\implies \cfrac{3+6\sqrt[3]{x^5}}{\sqrt[3]{x^4}}[/tex]
that'd be hmmm a kinda simplification of it, not sure if I could call it a simplified version, more like an expansion though.
