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sasogeek
Group Title
Prove that any number \(\huge n \) to the power 0 is equal to one.
\(\huge : n^0=1 \)
 2 years ago
 2 years ago
sasogeek Group Title
Prove that any number \(\huge n \) to the power 0 is equal to one. \(\huge : n^0=1 \)
 2 years ago
 2 years ago

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KingGeorge Group TitleBest ResponseYou've already chosen the best response.2
What about \(n=0\)? That's undefined.
 2 years ago

sasogeek Group TitleBest ResponseYou've already chosen the best response.0
make that exception, then prove for any other number
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Do you know that \(\Large \color{purple}{\rightarrow x^n \div x^1 = x^{n  1} }\)
 2 years ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.2
We know that \(n^1=n\) and \(n^{1}={1 \over n}\) for all \(n\). If we multiply together,\[n^1 \cdot n^{1}=n^{11}=n^0\]\[n\cdot{1 \over n}={n \over n}=1\]So \(n^0=1\)
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
\(\Large \color{purple}{\rightarrow x^1 = x }\) \(\Large \color{purple}{\rightarrow x^1 \div x^1 = 1 }\) as they cancel out. Also, x^1 over x^1 = x^0 \(\Large \color{purple}{\rightarrow x^0 = 1 = x^1 \div x^1 }\)
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
nice answers
 2 years ago

across Group TitleBest ResponseYou've already chosen the best response.0
@KingGeorge, I would say that for the case where \(n=0\) is more subjective than it is undefined nowadays. ;)
 2 years ago
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