### Instruction: What is the product of the positive integer divisors of 100?### Response: To find the product of the positive integer divisors of 100, I need to list them first.
I know that 100 is 2^2 times 5^2, so its divisors are of the form 2^a times 5^b, where a and b are 0, 1, or 2.
There are nine such divisors: 1, 2, 4, 5, 10, 20, 25, 50, and 100.
To find their product, I can multiply them in pairs that have the same product, such as 1 and 100, 2 and 50, 4 and 25, and so on.
This way, I get 100^4 times 10, which is 10^9.
Alternatively, I could use the fact that the product of the divisors of a number is the number raised to half the number of divisors.
Since 100 has nine divisors, this formula gives me 100^(9/2), which is also 10^9.