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Why can't we distribute the exponents over addition?

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Thinking about it this way, we know there is clearly some area that we are missing for every larger exponent. To figure out what that area is, we can simply expand. [math](a+b)^2 = a^2 + 2ab + b^2[/math]. So we have an area of [math]2ab[/math] missing for the case of n=2. read more

I understand that exponents don't distribute over addition and have seen plenty of examples i.e. $$ (x + y)^2\neq x^2 + y^2 $$ but I'm wondering why that is. read more

We can think of the value of an exponential function on the input 1 as the base of that exponential, even though it can turn out that different exponential functions take on the same value at 1 (e.g, as relates to the ambiguities noted above from the existence of multiple square roots). read more

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