Question

Which expression is equivalent to –8?

–2–3

(-1/2)^-3

(1/2)^-3

2–3

Answer 1

Answer: second option. (NOTE: If the first option is $(-2)^3$, then it would be an equivalent expression too, because:  $(-2)(-2)(-2)=-8$)

Step-by-step explanation:

To solve this problem you must keep on mind the following exponents rule:

$(\frac{1}{a})^-b=a^b$

Therfore, you have that:

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

This means that the number -2 must be multiply by itself three times. Therefore, you obtain the folllowing result:

$(-2)(-2)(-2)=-8$

If the first option is $(-2)^3$, then it would be an equivalent expression too, because:

 $(-2)(-2)(-2)=-8$

Answer 2

Answer:

$(\frac{-1}{2})^{-3} = -8$.

Step-by-step explanation:

Given :  –8.

To find : Which expression is equivalent.

Solution : We have given  –8.

By the radical rule : $(\frac{-1}{x})^{-a} = -x^{a}$.

Then

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

$(\frac{-1}{2})^{-3} = -8$.

Therefore,  $(\frac{-1}{2})^{-3} = -8$.