Answer
-8
Work Step by Step
part 1
(-n)^3
So we want the greatest value of n to make the result a positive integer ending in 2.
Part 2
(8)^3=8*8*8=512
(-(8))^3=(-8)*(-8)*(-8)=-512
First, we need a number that has a cube end in 2. So just go through and raise 0 through 9 to 3 and you'll see that 8 is 512. which has a 2 in the ones place. But if we plug in 8 for n, it is -512.
This is because we are multiplying by -8, 3 times. Multiplying two negatives together gets rid of the negative, but multiplying that by another negative puts the negative back.
part 3
(-(-8))^3=8^3=8*8*8=512
So, in order to get rid of that, we have to make n-8.
-8 is the largest negative number that ends with 8, so -8 will be the answer.
