I find it’s useful to interpret the exponent as “how many times you multiply 1 by the number. So 2^1 is 1 multiplied by 2 one time, i.e. 1 * 2. 2^0 is then 1 multiplied by 2 0 times, i.e. 1.
It also works with negative exponents, if we consider that dividing by a a given number one time is like multiplying by the same number minus-one time.
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