[SideburnsOfDoom]

You can visualise incrementation as a single step along a line, addition as a step of any length along the line.

Multiplication: the formula for area of a rectangle is "length times height", so IMHO now this - "a * b" is best visualised as 2d. Or if you like, "m lines of length n", visualised as a stack of lines.

Exponentiation covers "to the power of 2" (area of a 2d object) "to the power of 3" (volume of a 3d cube) and beyond, so now we've run out of graph dimensions.

I think what we can take from this, is that when going from first operation to second, second to third etc, the rate of change is not constant, it is increasing. Since the sequence is "no extra dimensions, one extra dimension, all the extra dimensions"