Answer:
[tex](-\frac{1}{2} )^{-3}[/tex]
Step-by-step explanation:
Let us apply the following law of exponents to simplify all the options.
[tex]a^{-m}=\frac{1}{a^{m}}[/tex]
For the first option, we have
[tex]-2^{-3}=\frac{1}{-2^3} =-\frac{1}{2\times 2\times 2\times 2} =-\frac{1}{8}[/tex]
For the second expression, we have,
[tex](-\frac{1}{2})^{-3}=\frac{1}{(-\frac{1}{2})^3}[/tex]
[tex]=\frac{1}{-\frac{1}{2}\times -\frac{1}{2} \times -\frac{1}{2} }[/tex]
[tex]=\frac{1}{-\frac{1}{8} }[/tex]
[tex]=-1\times \frac{8}{1}=-8[/tex]
For the third expression, we have,
[tex](\frac{1}{2})^{-3}=\frac{1}{(\frac{1}{2})^3}[/tex]
[tex]=\frac{1}{\frac{1}{2}\times \frac{1}{2} \times \frac{1}{2} }[/tex]
[tex]=\frac{1}{\frac{1}{8} }[/tex]
[tex]=1\times \frac{8}{1}=8[/tex]
For the last option, we have
[tex]2^{-3}=\frac{1}{2^3} =\frac{1}{2\times 2\times 2\times 2} =\frac{1}{8}[/tex]
Hence the correct answer is B.
