why is a number raise to the power zero always given to be equal to one.?
Answers
Answer:
because it comes under the class of zero exponents. The expression with the exponent as 0 is equal to 1 is referred as zero exponent.
Answer:
Since you would like to know this, I suppose you would
also like to know why n? = yn or n- = You've come to the right place.
First off, let me tell you that it is definition. n is defined to be 1. But it makes perfect sense why it was defined that way. But that is the question after all, isn't it? Why?
Why is it defined that way?
In high school you would have learnt that am x a" = am+", when m and n are integers. This should be obvious why. We would multiply a with itself m times and then multiply the whole thing with another na's, so in total, we would have multiplied a with itself m+n times. All good so far, right? Let's move on.
Then how do we define a? ? We need to define it since, otherwise, it is not clear what is meant by multiplying a with itself "half times". But how do we do it? What do we mean by such a thing? Whatever it means, one thing
must be clear: ai x ai must be equal, by the above relation, to a+ = a' = a. Basically, we want the above relationship to hold, where we said that exponents add. Now ai is such a number that when we multiply it with itself, we get a, which means a 2
must be the square root of a. Isn't that neat?