If s and t are integers greater than 1 and each is a factor of the integer n, which of the following must be a factor of n^{st} ?
1) s^t
2) (st)â²
3) s+t
a) none
b) 1 only
c) 2 only
d) 3 only
e) 1 and 2

E) 1 and 2

Step-by-step explanation:

We are given that there are two integers (s and t) and they are factors of another integer (n). For example if s = 3 and t = 2, we can have n = 6.

Thus:

n^(st) = 6^(2*3) = 6^6 = (2^6)(3^6)

For the first condition: s^t = 3^2 is a factor of (2^6)(3^6)

For the second condition: (st)^2 = (3*2)^2 = 6^2 is a factor of 6^6

For the third condition: s+t = 3+2 = 5 is not a factor of 6^6 or (2^6)(3^6)

Therefore, only 1 and 2 are factors of n^(st)