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0 power
this is math related, but it's not a homework question.
Okay, there's a simple rule that states anything to the zero power is 1. for example:
9 to the 0 power=1
why is that?? i understand how you get a 0 power, but why is it 1?? just curious.
thanks!!
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The ancient magicians who invented math decided that is how it would be.
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You know about subtracting powers? Like to simplify 5 to the fifth over five to the thrid, you subtract, and get 5 to the second, right?
Now let's say you have five to the fifth over five to the fifth. Anything over itself is one, and if you subtract the exponents, you get 5 to the 0 power, which is 1!
hope I didn't confuse you more =P
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My teacher explained this to me Friday=].
What you do is, say you take a sheet of paper, and it's your whole number.
You fold it once, and you have two boxes.
You fold it twice, and you have four boxes.
You fold it 3 times, and you have 8 boxes.
You fold it 4 times, and you have 16 boxes.
So if your fold it 0 times.. you have..1!
Get it?
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Lets start from the beginning.
9 to the third power is 9x9x9=729
9 to the second power is 9x9=81
9 to the first power is 9.
So, to find any positive power of 9, it's 9 multiplied by itself however many times the power is. You probably know all that.
So how do negative powers work?
How do you find 9 to the negative third? Since positive is the opposite of negative, you want to find the opposite answer as 9 to the third. To do this you take what's called the inverse of 9 to the third. To do this you flip the fraction upside down. The number 729 (729/1) flipped upside down is 1/729. So 9 to the negative third is 1/729 (about 0.00137).
Ok so make a list of the powers of 9 going from the negative third to the third.
1/729, 1/81, 1/9, 1, 9, 81, 729
There's a pattern. How do you get from 1/729 to 1/81? You multiply by 9. The same thing is true all the way up the list. You multiply by 9 to get the next answer. It only makes sense then, that to move to the LEFT in the list you would divide by 9 instead of multiply.
So, calculate 9 to the 0.
1/9 times 9 is 1 and 9 divided by 9 is also 1.
I hope this helps you understand why the answer is 1! I'm sorry if that was confusing or hard to follow. If you need me to explain something better let me know and I'll do my best. It's a hard concept to grasp, so don't overthink it. It's just part of a pattern. :)
Good call lostinpraise, I didn't even look for a website. The website explains it a bit better than I did. :-P
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[Link](Mouse over link to see full location)
This website explains exactly why, I read it through and I understood almost all of it, so I hope it helps!
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