Why is anything to the zero power = 1 ?

Answer 1

Any number raised to the power of zero is equal to 1 because it is defined that way. This definition is based on mathematical principles and is consistent with the properties of exponents.

One way to understand this is to consider the pattern of powers of a number. For example, if we have 2 raised to the power of 2, we get 2^2 = 2 x 2 = 4. If we continue this pattern, we have 2^3 = 2 x 2 x 2 = 8, 2^4 = 2 x 2 x 2 x 2 = 16, and so on. As we increase the power, we are essentially multiplying the base number by itself multiple times.

Now, if we start decreasing the power, we can see that dividing by the base number repeatedly will take us back to 1. For example, 2^1 = 2, 2^0 = 2 divided by 2 = 1. In this case, we can think of it as dividing 2 (the base number) by itself, which leads to 1.

This pattern holds true for any base number. When we raise any number to the power of zero, we are dividing that number by itself, which gives us 1. Therefore, anything to the power of zero is equal to 1 by definition.