2066 to the power any number(non-negative) has 6 in the units place.

for (2066)^z to divide 3176793, the only possible value of Z is 0 (as 2066^0 = 1.)

now (Z^X)-(X^Z)= (0^1)-(1^0) = -1 (B)

HTH!

In my experience when a variable is described as a "non-negative integer" there is a strong possibility that variable is 0.

They key to this problem is to recognize that 2,066 is not a factor of 3,176,793, so it wouldn't be a factor after being raised to a non negative integer UNLESS that non negative integer is 0. When any number is raised to the 0 power the result is 1, thus making it a factor of any other integer. Using this logic we have solved for Z = 0.

We also know that X is any positive integer.

Z^X = 0 since Z = 0.

X^Z = 1 since Z = 0.

0 - 1 = -1.


Even though this is the solution, this question is really testing your knowledge of the units place by giving you a convenient number ending in 6 since any integer ending in 6 raised to an integer power results in a number with a 6 in the units place. 3,176,793 has a 3 in it's unit place so we can quickly deduce that 2,066 is not a factor of 3,176,793.00