Question

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)²
3) s+t

A) None
B) 1 only
C) 2 only
D) 3 only
E) 1 and 2

Answer 1

Answer:

The answer is E) 1 and 2

Step-by-step explanation:

Given that s and t are greater than 1.

Let's assume that s = 4 and t = 2 and n = 8 (each on is a factor of the integer 8)

$n^{st} = 8^{8} = 4^{8} *2^{8}$

Now check for the options -

1)$4^{2}$ ( Can be a factor of  $n^{st} = 8^{8}$)

2) $(4*2)^{2} =8^{2}$ ( Can be a factor of  $n^{st} = 8^{8}$)

3) $4+2 = 6$ ( Cannot be a factor of  $n^{st} = 8^{8}$)

Thus, the option is E