To find the greatest common factor of these three terms, we need to factor each one and identify the highest power of each factor that is common to all three. Then, we can multiply those factors together to find the GCF.
Let's begin by factoring each term:
1/4n^2m^3 = (1/4) * n^2 * m^3
5/20n^7m^8 = (1/4) * n^7 * m^8
3/12n^2m^8 = (1/4) * n^2 * m^8
Now, we can see that each term has a common factor of 1/4, so we can factor that out:
1/4 * (n^2 * m^3)
1/4 * (n^7 * m^8)
1/4 * (n^2 * m^8)
To find the highest power of each factor that is common to all three terms, we need to look at the exponents. The highest power of "n" that is common to all three terms is 2, and the highest power of "m" that is common to all three terms is 3. Therefore, the GCF is:
1/4 * n^2 * m^3
This simplifies to:
n^2m^3/4
So, the correct option is (c) n^2m^3/4.