MATPC 100G Week 5 Shorthand! An obvious, though new idea

To me the idea that multiplication and exponents are actually shorthand for serialized addition, etc.  This week's instructor mentioned something I never realized before.  The fundamental reason for the order of operations starting with exponents and ending with addition and subtraction is that it is exponents and multiplication/division are levels of shorthand!

Exponents are shorthand for multiplication/division and multiplication/division is shorthand for addition/subtraction.  This along with the carry over operations of each digit in an arithmetic operation may be the key to my success in creating my own infinite, multi-base calculator for use in my shell that I am creating.  If I create a calculator that can operate to virtually any number of digits, both high and low via a simple shell option and a digits precision variable, then I may produce better results script calculations and operations.  Eventually, if I can compile these shell script operations into a portable Ada standard form that can be used by the shell on any system, like a Z Shell word-code program, then both program and library distribution can become faster and more portable, even though each operating system gets the work done differently.  This will allow 128 bit or more calculations on even a 32-bit machine, though it will be significantly slower than it would be on a 128 bit machine.

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