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Power (Joules) = the square root of the voltage squared divided by the resistance
The 3 stands for cubed. It would be used to express volumes.
Yes, that's a shortcut often used for powers of functions. Please note that for the special case of function to the power minus 1 of x there is a different definition - it is usually taken to mean the inverse function. So, if you want to write the reciprocal of a function, you have to express it in a different way.
It means six squared, or 6 times 6. 6 is used as a factor twice. The value is 36.
It is the pythagorean theorem. Used in finding the lengths of sides of right angled triangles.