SOLUTION: Explain why 2 to the -3 power equals to 1 over 2 to the 3 power?

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Question 112650: Explain why 2 to the -3 power equals to 1 over 2 to the 3 power?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
2%5E-3
What do I get if I multiply by 2%5E3?
%282%5E-3%29%282%5E3%29+=+2%5E%28-3+%2B+3%29
%282%5E-3%29%282%5E3%29+=+2%5E0
2%5E0+=+1
Now what do I get if I multiply 1+%2F+2%5E3 by 2%5E3?
%281+%2F+2%5E3%29%2A%282%5E3%29+=+1
I can replace the 2 by any other number and the 3 by any other
number and this is still true.
2%5E-3+=+1+%2F+2%5E3