Anything multiplied by 0 is 0 right so why does x number raised to the power of 0 = 1? isnt it x^0 = x*0 (im turning grade 10 and i asked my teacher about this he told me its because its just what he was taught 💀)
In: Mathematics
Anything multiplied by 0 is 0 (x * 0 = 0) – but why is that so? Because multiplying means addition multiple times, for example x*4 = x + x + x + x. Or you could say x*4 is first adding x three times, then adding x one more time: x*4 = x*3 + x*1. So far pretty obvious, so what if I wanted to say the same about 0? “Y*ou could say x*4 is first adding four times, then adding zero more times*”: x*4 = x*4 + x*0. For this last equivalence to be true, x*0 must be 0.
Now let’s rewrite exactly the same as above, but for power instead of multiplication:
Anything raised to the 0-th power is 1 (x^0 = 1) – but why is that so? Because power means multiplying multiple times, for example x^4 = x * x * x * x. Or you could say x^4 is multiplying by x three times, then multiplying by x one more time: x^4 = x^3 * x^1. So far pretty obvious, so what if I wanted to say the same about 0? “Y*ou could say x^4 is first multiplying four times, then multiplying zero more times*”: x^4 = x^4 * x^0. For this last equivalence to be true, x^0 must be 1.
The reasons in both cases are the same.
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