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 o…

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

The answer is E) 1 and 2

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