Suppose you have a square with side $s.$ You want to measure the area of the square. Everyone knows, of course that for a square, $A=s^2.$ It can be shown, using calculus, that in general, if

$y=x^a$ then ${}_y=a{}_x$

You measure the side of your square and evaluate its uncertainty by determining the standard deviation. It turns out that $s=(10\mathrm{.}00+-0\mathrm{.}03)cm.$ Calculate $A,{}_s,{}_A,$ and ${}_A.$