Question

Which expression is equivalent to -8?

Answer 1

Answer:

$(-\frac{1}{2} )^{-3}$

Step-by-step explanation:

Let us apply the following law of exponents to simplify all the options.

$a^{-m}=\frac{1}{a^{m}}$

For the first option, we have

$-2^{-3}=\frac{1}{-2^3} =-\frac{1}{2\times 2\times 2\times 2} =-\frac{1}{8}$

For the second expression, we have,

$(-\frac{1}{2})^{-3}=\frac{1}{(-\frac{1}{2})^3}$

$=\frac{1}{-\frac{1}{2}\times -\frac{1}{2} \times -\frac{1}{2} }$

$=\frac{1}{-\frac{1}{8} }$

$=-1\times \frac{8}{1}=-8$

For the third expression, we have,

$(\frac{1}{2})^{-3}=\frac{1}{(\frac{1}{2})^3}$

$=\frac{1}{\frac{1}{2}\times \frac{1}{2} \times \frac{1}{2} }$

$=\frac{1}{\frac{1}{8} }$

$=1\times \frac{8}{1}=8$

For the last option, we have

$2^{-3}=\frac{1}{2^3} =\frac{1}{2\times 2\times 2\times 2} =\frac{1}{8}$

Hence the correct answer is B.

Answer 2

Answer:

The answer is B,

Step-by-step explanation:

I got it right on the test