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What if you raised 0 to the power of 2?

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    $\begingroup$ $x^n$ for any $n$ is a polynomial with a unique root at $x=0$ with multiplicity $n$. $\endgroup$ – klein4 Apr 18 at 3:26
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    $\begingroup$ $0^2$ means $0 \times 0$ , and $0$ times anything is $0$. Likewise $0^3 = 0 \times 0^2$ equals $0$ as well. $\sqrt{0} \times \sqrt{0} = 0$ by definition of square root, so that is $0$ as well. $\endgroup$ – RobertTheTutor Apr 18 at 3:27
  • $\begingroup$ $0^2$ would be $0 \times 0$. Which is, of course, equal to $0$. And $0^3 = 0\times 0 \times 0$ and $0^k$ for any positive whole number would be $\underbrace{0\times 0 \times .... \times 0}_{k \text{ times}}$ which are also obviously equal to $0$. $\endgroup$ – fleablood Apr 18 at 3:36
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Well for any $x$, $x^2=x\times x$. And so setting $x=0$, $0^2=0\times 0=0$. Alternatively you can generalise this. $$x^n=x\times x\times \cdots \times x$$ $n$ times. And for any $n>0$. Setting $x=0$ you get $0$ :). I hope this helps.

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