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
You put 1000 bucks in a bank with an annual interest rate of 5%.
How much do you have after *n* years?
After 1 year, it’s 1000*1,05=1050.
After two years, it’s 1000*1,05*1,05=1102,5.
And so on.
After *n* years it’s 1000*1,05*^(n)*. So the 1,05*^(n)* expresses how much your capital has multiplied after *n* years.
What’s 1,05^(0) then? It’s how much your capital multiplied after 0 years, i.e. you put it in and immediately withdrawn. Obviously, it’s the same amount, so it’s multiplied by 1. That’s why 1,05^(0)=1.
It works the same way regarldess of what the annual interest rate is, so that’s why x^(0)=1 for any x.
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