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

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

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

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

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.2We 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 \(n^0=1\)

ParthKohli
 3 years ago
Best 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 \(\Large \color{purple}{\rightarrow x^0 = 1 = x^1 \div x^1 }\)

across
 2 years ago
Best 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. ;)
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