To find the value of the expression given we need to remember that following properties:
[tex]\begin{gathered} a^{-n}=\frac{1}{a^n} \\ \frac{1}{a^{-n}}=a^n \end{gathered}[/tex]
Using this properties, we can find the value of the expression. To do this we plug the values of x and y given:
[tex]\begin{gathered} \frac{1}{2^{-2}(2)^{-3}(-4)^5}=\frac{2^2(2)^3}{(-4)^5} \\ =\frac{4\cdot8}{-1024} \\ =-\frac{32}{1024} \\ =-\frac{1}{32} \end{gathered}[/tex]
Therefore the answer is C.
