What's the easiest way to clean concrete
Hydrogen peroxide is an extremely effective cleaner. Often it is marketed as "sodium percarbonate", "non-chlorine bleach" and "oxygen bleach". You can get it in powder form or liquid form. Either might be just as good, but the higher the hydrogen peroxide concentration, the better of a job it will do.

If you get powder, I recommend sprinkling it onto the concrete, then getting it damp. You can then smooth the wet mixture evenly over the concrete to get even coverage. If you get liquid, just spread evenly. Either way, let it sit for 5 - 15 minutes, then wash away. Repeat as necessary. Once it has stopped foaming, I think the hydrogen peroxide has finished reacting and won't clean any more. So, if there is still dirt left, you'll need to apply another wash of cleaner.

Hydrogen peroxide is relatively safe, but it does kill red blood cells quite quickly. I've watched drops of it on my hand reduce the blood in that area inside my skin to white foam. So, if you get powder, avoid inhaling it, but aside from that, the only off-gassing is pure oxygen. 

My parents had a hard time cleaning mildew off our porch and power washing didn't work. However, powdered hydrogen peroxide did work when used as I describe above.