Exponential bounds for monochromatic sums equal to products

We show that any $r$-coloring of $\{1,\mathrm{.}\mathrm{.}\mathrm{.},r^{r^{r^{3r}}}\}$ contains monochromatic sets $\{a,b,a+b,x,y,xy\}$ with $a+b=xy\mathrm{.}$