To simplify the expression
[tex]\frac{4x^{-3}}{-8x^{-4}}[/tex]we make use of a property of exponents that
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]Using the above property, our expression can be written as
[tex]-\frac{4}{8}x^{-3-(-4)}[/tex]which simplifies to
[tex]\begin{gathered} -\frac{1}{2}x^1 \\ \end{gathered}[/tex][tex]=-\frac{x}{2}[/tex]which is our answer!
