From the consecutive integers -10 to 10, inclusive…
This problem is testing our knowledge of the multiplication rules for positive and negative numbers. Remember that when we multiply an even number of negative numbers together the result is positive and when we multiply an odd number of negative numbers together the result is negative.
Because we are selecting 20 numbers from the list, we want to start by selecting the smallest 19 numbers we can and multiplying those together. In our list the smallest number we can select is -10. So we have:
(-10)^19 (Note that this product will be negative.)
Since we need to select a total of 20 numbers we must select one additional number from the list. However, since the final product must be as small as possible, we want the final number we select to be the largest positive value in our list. The largest positive value in our list is 10. So the product of our 20 integers is:
(-10)^19 x 10 (Note that this product will still be negative.)
This does not look identical to any of our answer choices. However, notice that
(-10)^19 can be rewritten as -(10)^19, so
(-10)^19 x 10 = -(10)^19 x (10)^1 = -(10)^20.