+2446 As a generalization, \(x^0=1\hspace{1cm},x\neq0\)
This table may help you understand why 3^0=1
| \(3^{10}\) | 3*3*3*3*3*3*3*3*3*3 | \(59049\) | |
|---|---|---|---|
| \(3^9\) | 3*3*3*3*3*3*3*3*3 | \(19683\) | |
| \(3^8\) | 3*3*3*3*3*3*3*3 | \(6561\) | |
| \(3^7\) | 3*3*3*3*3*3*3 | \(2187\) | |
| \(3^6\) | 3*3*3*3*3*3 | \(729\) | |
| \(3^5\) | 3*3*3*3*3 | \(243\) | |
| \(3^4\) | 3*3*3*3 | \(81\) | |
| \(3^3\) | 3*3*3 | \(27\) | |
| \(3^2\) | 3*3 | \(9\) | |
| \(3^1\) | 3 | \(3\) | |
| \(3^0\) | ? | ? |
Do you notice a pattern? I do. As you go down the list, you can divide by three to get to the next value. Therefore, if 3^1=3, all you have to do to get the next value is to divide by three. 3^1/3=1, so 3^0=1.
Here's another way of thinking about it. This method works for any number to the power of 0:
\(1=\frac{x^n}{x^n}=x^{n-n}=x^0\hspace{1cm},x\neq0\)
.
