If all parentheses are placed correctly, then [4(2m)^2] / [(4 * 10^-3m)^2] = 10^6 (meters cancel), not 2 * 10^6m.
This is less a question of physics and more one of the mathematical minutes, so please bear with me if this is a really dumb question. I am trying to understand an example equation in the textbook that went from [4(2m)^2] / [(4 * 10^-3m)^2] = 2 * 10^6m. It doesn't bother to explain the stages of the simplification, i.e. how it went from the left side to the right side.
I tried doing [4(2m)^2] / [16(10^-3m)^2] = (4m^2) / [4(10^-6m)] = (1m^2) / (10^-6m) but I'm stuck there. Any help would be greatly appreciated.
Ohh, I'm so sorry, I typed in the wrong equation. I feel absolutely foolish now... Here is the direct scan:
And here is my feeble attempt: [ 4 (2m)^3 ] / (4 * (10)^-3m)^2 = [ 4 (8m^3) ] / [ 16 (10^-6m^2) ] = (8m^3) / [ 4 (10^-6m^2) ] = (2m^3) / (10^-6m^2) = (2m^3) (10^6m^-2) = 2 * 10^6m
I am not too certain about the final two steps, did I do it right? Thank you so much for being patient with me!