sasogeek
  • sasogeek
Prove that any number \(\huge n \) to the power 0 is equal to one. \(\huge : n^0=1 \)
Mathematics
jamiebookeater
  • jamiebookeater
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KingGeorge
  • KingGeorge
What about \(n=0\)? That's undefined.
sasogeek
  • sasogeek
make that exception, then prove for any other number
ParthKohli
  • ParthKohli
Do you know that \(\Large \color{purple}{\rightarrow x^n \div x^1 = x^{n - 1} }\)

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KingGeorge
  • KingGeorge
We know that \(n^1=n\) and \(n^{-1}={1 \over n}\) for all \(n\). If we multiply together,\[n^1 \cdot n^{-1}=n^{1-1}=n^0\]\[n\cdot{1 \over n}={n \over n}=1\]So \(n^0=1\)
ParthKohli
  • ParthKohli
\(\Large \color{purple}{\rightarrow x^1 = x }\) \(\Large \color{purple}{\rightarrow x^1 \div x^1 = 1 }\) as they cancel out. Also, x^1 over x^1 = x^0 \(\Large \color{purple}{\rightarrow x^0 = 1 = x^1 \div x^1 }\)
UnkleRhaukus
  • UnkleRhaukus
nice answers
across
  • across
@KingGeorge, I would say that for the case where \(n=0\) is more subjective than it is undefined nowadays. ;)

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