### Instruction: What is the product of the positive integer divisors of 100?### Response: I know that the positive integer divisors of 100 are the numbers that divide 100 evenly, without leaving a remainder.
To find them, I can start by listing the smallest and largest ones: 1 and 100 are divisors of 100.
Then I can try the next smallest and largest ones: 2 and 50 are divisors of 100.
I can continue this process until I meet in the middle: 4 and 25, 5 and 20, 10 and 10 are all divisors of 100.
I notice that I have listed 9 divisors in total, and they form pairs that multiply to 100, except for 10, which is paired with itself.
This means that the product of all the divisors is the same as the product of 100 raised to the power of half the number of divisors.
In other words, the product of the positive integer divisors of 100 is 100^(9/2).