Question

Which expression is equivalent to –8?

–2–3

(-1/2)^-3

(1/2)^-3

2–3

Answer 1

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

Explanation:

Given : –8.

To find : Which expression is equivalent.

Solution : We have given –8.

By the radical rule :
`((-1)/(x))^(-a) = -x^(a)`.

Then

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

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

Therefore,
`((-1)/(2))^(-3) = -8`.

Answer 2

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

Explanation:

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

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

Therfore, you have that:

`(-(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`