I'm studying for a test I have this week and a practice question asks whether or not the price elasticity of demand for the demand function $\ q = Ap^{-x} $, where A and x are positive constants depends on the price p.
I've attempted to use the equation, $ \frac{dQ}{dP}*\frac{P}{Q} $ in order to solve the problem and I am getting the result,
$ \epsilon = \frac{-xA}{p^{x+1}}*\frac{p}{q} = \frac{-xA}{p^{x}q}$
Which would mean that the elasticity does depend on p, however the answer in my practice exam says that it does not depend on p. Why is that the case/where did I go wrong?