# Why does zero raised to any positive power equal zero? [closed]

What if you raised 0 to the power of 2?

• $x^n$ for any $n$ is a polynomial with a unique root at $x=0$ with multiplicity $n$. – klein4 Apr 18 at 3:26
• $0^2$ 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. – RobertTheTutor Apr 18 at 3:27
• $0^2$ 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 $0$. – fleablood Apr 18 at 3:36

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.