Given:
[tex]\frac{x^{-4}}{x^3}[/tex]
To simplify the given expression, we use the Quotient Rule first:
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
Based on this, our expression would be:
[tex]\frac{x^{-4}}{x^3}=x^{-4-3}[/tex]
Next, we simplify:
[tex]\begin{gathered} =x^{-7} \\ \end{gathered}[/tex]
Then, we use the Negative Power Rule:
[tex]x^{-a}=\frac{1}{x^a}[/tex]
So,
[tex]x^{-7}=\frac{1}{x^7}[/tex]
Therefore, the answer is:
[tex]\frac{1}{x^7}[/tex]
