[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}}}}\\\\
-------------------------------[/tex]
[tex]\bf \cfrac{1}{2}(2x^2-8)+\cfrac{1}{3}(6x^{-3})\implies \cfrac{2x^2-8}{2}+\cfrac{6x^{-3}}{3}\implies \cfrac{2x^2}{2}-\cfrac{8}{2}+\cfrac{6}{3}\cdot \cfrac{1}{x^3}
\\\\\\
x^2-4+2\cdot \cfrac{1}{x^3}\implies x^2-4+ \cfrac{2}{x^3}\implies \cfrac{(x^3\cdot x^2)-(x^3\cdot 4)+2}{x^3}
\\\\\\
\cfrac{x^{3+2}-4x^3+2}{x^3}\implies \cfrac{x^5-4x^3+2}{x^3}[/tex]
