proof that x^0 = 1

x5
------------- =
X5

x*x*x*x*x
----------- = 1 =
x*x*x*x*x

x5-5 = x0 = 1

To prove that x^0 = 1, we can use the fact that any number divided by itself is equal to 1.

Let's consider x raised to the power of 5, denoted as x^5.

We can write x^5 as x * x * x * x * x.

Now, if we divide x^5 by x^5, we get:

(x * x * x * x * x) / (x * x * x * x * x).

According to the properties of division, when we divide two numbers with the same base, we subtract the exponents.

So, we can rewrite this as:

x^(5-5).

When we subtract 5 from 5, we get 0.

Therefore, we have:

x^0 = 1.

Hence, we have proven that x^0 is equal to 1.