This is the proof http://planetmath.org/encyclopedia/ProofOfPropertiesOfTheExponential.html [Broken] I wonder what they do when they describe monotnicity for integers. Why is [tex]x^p<y<p[/tex] when x<y and p is a positive integer? What if p was really large? and further down in the part homogeneity for rational exponents is there a typo there? Should not [tex] (v_1 v_2)^n > (xy)^m[/tex] and not [tex] (v_1 v_2)^n < (xy)^m[/tex] or?