Question

Which expression is equivalent to -8?

Answer 1

The answer is B,

Explanation:

I got it right on the test

Answer 2

`(-(1)/(2) )^(-3)`

Explanation:

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

`a^(-m)=(1)/(a^(m))`

For the first option, we have

`-2^(-3)=(1)/(-2^3) =-(1)/(2* 2* 2* 2) =-(1)/(8)`

For the second expression, we have,

`(-(1)/(2))^(-3)=(1)/((-(1)/(2))^3)`

`=(1)/(-(1)/(2)* -(1)/(2) * -(1)/(2) )`

`=(1)/(-(1)/(8) )`

`=-1* (8)/(1)=-8`

For the third expression, we have,

`((1)/(2))^(-3)=(1)/(((1)/(2))^3)`

`=(1)/((1)/(2)* (1)/(2) * (1)/(2) )`

`=(1)/((1)/(8) )`

`=1* (8)/(1)=8`

For the last option, we have

`2^(-3)=(1)/(2^3) =(1)/(2* 2* 2* 2) =(1)/(8)`

Hence the correct answer is B.