Answer:
The equivalent expression is;
[tex]\frac{1}{x^{19}}[/tex]
Explanation:
Given the expression;
[tex]\frac{(x^{-5})^4}{x^{-1}}[/tex]
we want to simplify;
[tex]\begin{gathered} \frac{(x^{-5})^4}{x^{-1}} \\ =\frac{x^{-5}^{(4)}}{x^{-1}} \\ =\frac{x^{-20}}{x^{-1}} \end{gathered}[/tex]
Applying the rules of exponent;
[tex]\begin{gathered} =\frac{x^{-20}}{x^{-1}} \\ =\frac{1}{x^{20}}\times\frac{1}{x^{-1}} \\ =\frac{1}{x^{20-1}} \\ =\frac{1}{x^{19}} \end{gathered}[/tex]
Therefore, the equivalent expression is;
[tex]\frac{1}{x^{19}}[/tex]
