It's not true for all real numbers p and q. For example if p = 1/2 and q = -1 the left hand side is less than the right hand side for odd values of the exponent.

I suspect the problem should have been written "forpositivereal values of p and q..." In this case you can show that p = q/(q-1) and that p and q are both > 1. The equation boils down to , where 'n' is the exponent (2013 in this case).