Question

Show that 2 power 0 is equal to 1

Answer 1

2 power 0 is equal to 1 by definition, if we want to use power rules. For example, let's divide $2^n$ by $2^n$ where $n$ is any number. It is clear, that

$$\dfrac{2^n}{2^n} = 1$$

But, on the other hand, using power rules, obtain:

$$\dfrac{2^n}{2^n} = 2^{n-n} = 2^0$$

Thus for the sake of consistency it should be $2^0 = 1$.