Question

Show that 2°is equal to 1

Answer 1

We all know the rule:

$$\frac{a^x}{a^y}=a^{x-y}.$$

Consider this:

$$\frac{2^x}{2^y}=2^{x-y}.$$

Now, consider this:

$$\frac{2^x}{2^x}=2^{x-x}=2^0.$$

But what is $2^x/2^x$?

According to the definition of power x:

$$2^x=2·2·2·...·2·2\text{ (the number of 2 used is }\textit{x}\text{)}.$$

So, since we take the same number of 2s and divide it by the equal number of 2, we divide a value by itself, which gives 1. Thus, $2^0=1$.