(From my 11th/12th grade math homework) Can you give me an explanation to why ba^(x+Δx)/ba^x = ba^Δx?

I assume ba is a single variable name, not b*a.

 

From the laws of indices (powers) we have z^m*zⁿ = z^m+n

For example think of 2³*2² = 2*2*2*2*2 = 2⁵ = 2³⁺²

 

In your case  ba^x+Δx = ba^x*ba^Δx, so if you divide this by ba^x you are left with ba^Δx