Answer:
[tex]\huge\boxed{\bf\:64}[/tex]
Step-by-step explanation:
[tex]\left(\frac{(-1)^{5}}{\left(-2\right)^{-3}}\right)^{2}[/tex]
Now, simplify [tex](-1)^{5} = -1[/tex]. Then,
[tex]\left(\frac{-1}{\left(-2\right)^{-3}}\right)^{2}[/tex]
Calculate: [tex](-2)^{-3} = \frac{1}{(-2)^{3}} = - \frac{1}{8}[/tex].
[tex]\left(\frac{-1}{-\frac{1}{8}}\right)^{2}[/tex]
Divide [tex]-1[/tex] by [tex]- \frac{1}{8}[/tex]. The result will be [tex]8.[/tex]
[tex]\left(-\left(-8\right)\right)^{2} \\= 8^{2}[/tex]
Calculate [tex]8[/tex] to its square which is [tex]64.[/tex]
[tex]8^{2}\\=\boxed{\bf\: 64} \: \:\mathrm{(3^{rd} \: option)}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
