Final answer:
To compute (-8)^{-2/3}, find the cube root of 8, square it, and then take the reciprocal due to the negative exponent. Thus, the result of this expression is 1/4.
Step-by-step explanation:
To compute the expression (-8)^{-2/3}, we can break it down into two steps. First, the exponent -2/3 means we take the cube root and then square it. Secondly, because the exponent is negative, we will take the reciprocal of the result.
- Find the cube root of 8, which is 2 (Notice that we take the positive cube root of a positive number even though our base is negative; we will consider the negative sign after).
- Since the base is negative and the exponent -2/3 suggests an even power, the overall result will be positive. So, we have the cube root of negative eight being negative two (-2).
- Square the result of the cube root: (-2)^2 = 4.
- Because the exponent is negative, we take the reciprocal of 4, which is ⅓.
Therefore, (-8)^{-2/3} = ⅓.