5. Why is anything to the zero power = 1 ?

Answer 1

To understand why anything to the zero power equals 1, we can approach it through exponentiation and the rules of exponents.

When we raise a number to a certain power, we are essentially multiplying that number by itself the specified number of times. For example, 2 to the power of 3 is written as 2^3 and is equal to 2 * 2 * 2 = 8.

Now, let's consider the pattern as we raise 2 to different powers:

2^3 = 2 * 2 * 2 = 8
2^2 = 2 * 2 = 4
2^1 = 2

Notice that as we decrease the power, the result is halved. Continuing this pattern:

2^0 = ?

Let's think about what this means. When we raise a number to the power of 0, we are essentially asking: how many times do I need to multiply the number by itself to get 1? In this case, we want to find how many times we need to multiply 2 by itself to get 1. There is no way multiplying any number by itself would result in 1 except when the number itself is 1. Thus, 2^0 should be equal to 1.

This logic can be extended to any number raised to the power of 0. Any non-zero number raised to the power of 0 will result in 1 because there is no way to multiply any number (except 1) by itself to equal 1. Therefore, anything to the power of 0 is defined as 1 based on this convention and mathematical consistency.