Because it is defined this way. Return to the definition of exponents in your textbook or read here:
Exponentiation - Wikipedia, the free encyclopedia
I know that any number raised to the zero power is 1.
I also know that any number raised to the 1st power is the number itself.
Sample A:
Let x = a number
Then x^(0) = 1....Wny is this the case?
Sample B:
Let y = a number
Then y^(1) = y....Why is this the case?
Teachers never explain this in terms that students can understand.
How about you?
How would you EASILY teach the above concepts in a classroom?
Because it is defined this way. Return to the definition of exponents in your textbook or read here:
Exponentiation - Wikipedia, the free encyclopedia
Most students think this. And, unfortunately, the exams that they're given usually perpetuate and reinforce this viewpoint.
There's always an uproar when an examination has questions different to the ones that have appeared on previous examinations. The usual objection is that this is unfair because they hadn't learned that sort of question. At this point I usually remark that my heart bleeds and reach for my violin.
x^0 = 1
If you have no power at all (so 0 power), you're still that one ( 1 ) powerless being
Exception: If you have no value at all ( 0 ) and no power at all, how would you be defined? Not!
y^1 = y
If your power is 1, no matter how much you jump around and stuff, you'll always be yourself
Et voila!
You probably know that anything to the 0 power is 1. But now you can see why. Consider .
By the division rule, you know that
.
But anything divided by itself is 1, so . Things that are equal to the same thing are equal to each other: if is equal to both 1 and , then 1 must equal . Symbolically,
There’s one restriction. You saw that we had to create a fraction to figure out . But division by 0 is not allowed, so our evaluation works for anything to the 0 power except zero itself.
There’s nothing mysterious! An exponent is simply shorthand for multiplying that number of identical factors. So is the same as (4)(4)(4), three identical factors of 4. And is just three factors of y, (y)(y)(y). In a similar fashion, means y is used as a factor 1 time, and since 1 is always a factor of any number we have: