We have k*a^n = 8!, k is a positive integer constant and the integers a and n are greater than 1. What is a?abhasjha wrote:.if the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n, what is the value of a?
(1) a^n = 64
(2) n = 6
(1) For the integers a and n greater than 1, we have more than one way to show that a^n = 64; 2^6 = 64, 4^3 = 64, and 8^2 = 64. Insufficient
(2) If n = 6, a^6 can be a factor of 8! for both rational and irrational a. Insufficient
Combine the two
n = 6 is possible only when a = 2.
[spoiler]C[/spoiler]
