Using this example, explain why any nonzero number raised to a power of zero is equal to one.(1 point)
Let's take the example of 2 raised to the power of 0, which is written as 2^0.
According to the basic rules of exponents, any nonzero number raised to the power of 0 is equal to 1.
To understand why, we can look at the pattern of exponents. When we raise 2 to increasing powers, we get:
2^0 = 1
2^1 = 2
2^2 = 4
2^3 = 8
As we can see, the value of 2 raised to increasing powers gets larger and larger. However, when we raise 2 to the power of 0, it becomes 1.
This pattern can be generalized to any nonzero number. When a nonzero number is raised to the power of 0, it essentially means that we are not multiplying the number by itself at all. We are multiplying it zero times.
In any multiplication, when we multiply any number by 0, the result is always 0. However, when we multiply any number by 1, the result is always that number itself.
So, raising any nonzero number to the power of 0 is essentially multiplying it zero times, which equals 1. This is why any nonzero number raised to the power of 0 is equal to 1.