Final answer:
The expression evaluates to -4i multiplied by the cube root of 2, resulting in a complex number. However, the given answer options suggest that real numbers may have been expected, indicating a potential misunderstanding in the problem's setup.
Step-by-step explanation:
To evaluate -√(-16) × ∛2, we first consider each operation individually. The square root of a negative number involves an imaginary number 'i' where i equals the square root of -1. Therefore, the square root of -16 is 4i because i² = -1 and 4² = 16.
Next, we calculate the cube root of 2, which is simply the number that when multiplied by itself three times equals 2. The cube root of 2 is approximately 1.2599, but since we do not need to be that precise, we'll consider the cube root of 2 remains as it is, ∛2.
Now, we multiply -4i by ∛2 to get the answer. Since multiplication is commutative, the order doesn't affect the product. Therefore, the expression becomes -4i × ∛2.
However, according to the given options, it seems there might have been an error made in the assumption that we're dealing with real numbers. The given options suggest the values should be real, but we derived a complex number. It's crucial to check the problem statement and confirm whether complex numbers are considered.