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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 [tex]n^{st}[/tex] ?
1) [tex]s^t[/tex]
2) (st)²
3) s+t

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

Respuesta :

nicorojascalvo

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)

[tex]n^{st} = 8^{8} = 4^{8} *2^{8}[/tex]

Now check for the options -

1)[tex]4^{2}[/tex] ( Can be a factor of  [tex]n^{st} = 8^{8}[/tex])

2) [tex](4*2)^{2} =8^{2}[/tex] ( Can be a factor of  [tex]n^{st} = 8^{8}[/tex])

3) [tex]4+2 = 6[/tex] ( Cannot be a factor of  [tex]n^{st} = 8^{8}[/tex])

Thus, the option is E

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