Problem Solving (PS) | Re: If n is an integer such that (-3)^(-4n) > 3^(6 - n), which of the

In theinequality

\( (-3)^{-4n} >3^{6-n}\)

we're raising the left side to an even power, so it's going to become positive in the end, and we can ignore the negative sign. Once we do that, we have equal positive integer bases on both sides (and our bases are greater than 1), and the left side will exceed the right precisely when the exponent on the left exceeds the exponent on the right. So

-4n > 6 - n
-6 > 3n
-2 > n

So n is definitely negative here, so cannot be prime, and is certainly less than 3. So II and III must be true. There's no way to tell if n is even, however. So D is theanswer.