aazt wrote:
If x and y are integers and \(x^y\)=256, what is the number of the different values of \(y^x\)?
Options:
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Hi,
256 has only 2 as a factor.
256=\(2^8=4^4=16^2=256^1\) ...
Those with even power can have x as NEGATIVE too..
So values can be\(2^8....(-2)^8....4^4....(-4)^4.....16^2....(-16)^2.....256^1\) ..
So\(y^x\) can be
8^2=64
8^{-2}=1/64
4^4=256..
4^(-4)=1/256
2^16
2^(-16)
1^256=1
So 7 values..
D
...
