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

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KingGeorgeBest ResponseYou've already chosen the best response.2
What about \(n=0\)? That's undefined.
 one year ago

sasogeekBest ResponseYou've already chosen the best response.0
make that exception, then prove for any other number
 one year ago

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

KingGeorgeBest 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 \(n^0=1\)
 one year ago

ParthKohliBest 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 \(\Large \color{purple}{\rightarrow x^0 = 1 = x^1 \div x^1 }\)
 one year ago

acrossBest 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. ;)
 one year ago
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