SOLUTION: Explain the Law of Exponents that states a to the -n power = 1 divided by a to the n power?

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Question 717186: Explain the Law of Exponents that states a to the -n power = 1 divided by a to the n power?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
You probably understand the positive exponents:
a%2Aa+=+a%5E2, a%5E2%2Aa=a%5E3, a%5E3%2Aa=a%5E4, a%5E4%2Aa=a%5E5, ...

To help us understand negative exponents, let's think about the opposite of the above. Instead of starting with a and repeatedly multiplying by a, think about starting with a high power of a and repeatedly dividing by a:
a%5E5%2Fa+=+a%5E4, a%5E4%2Fa+=+a%5E3, a%5E3%2Fa+=+a%5E2, a%5E2%2Fa+=+a%5E1...
As we did this the exponents kept going down by 1. Now, let's keep going!
a%5E1%2Fa+=+1+=+a%5E0 The exponent went down by 1 again!
a%5E0%2Fa+=+1%2Fa+=+a%5E%28-1%29 again, the exponent went down by 1
a%5E%28-1%29%2Fa+=+%281%2Fa%29%2Fa+=+1%2Fa%5E2+=+a%5E%28-2%29
etc.