Representing any number in $R_+$ by means of two numbers I have the following question:
Let $R_+$ denote the nonnegative reals. Let $0<a<1$ and $b>0$, and set $p = a^n b^m$. Is it possible to find a $n,m\in N$ such that $p$ can approximate any number in $R_+$ arbitrarily close?

This cannot be true in general, because a simple counter-example:
Set $a=\frac{1}{2}$ and $b=2$. Now, the only number that can be arbitrarily approximate is $0$, as is easily seen. 
But I believe that it could be true when $\frac{a}{b}$ is irrational. 
