SOLUTION: can you explain the six laws of exponents with explanations of each one?

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Question 25907: can you explain the six laws of exponents with explanations of each one?
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
1. %28a%5Em%29%28a%5En%29+=+a%5E%28m%2Bn%29

eg %28a%5E3%29%28a%5E2%29+=+a%5E5 means (axaxa) x (axa) which is axaxaxaxa --> a%5E5

2. %28a%5Em%29%2F%28a%5En%29+=+a%5E%28m-n%29

eg %28a%5E5%29%28a%5E2%29+=+a%5E3 means (axaxaxaxa) divided by (axa) which is axaxa --> a%5E3

3. %28a%5Em%29%5En+=+a%5E%28mn%29

eg %28a%5E3%29%5E2+=+a%5E6 means (axaxa) x (axaxa) which is axaxaxaxaxa --> a%5E6

4. a%5E0+=+1

eg %28a%5E3%29%2F%28a%5E3%29+=+1 means (axaxa)/(axaxa) which is 1...but the powers in a division subtract, so we get 3-3 which is zero. The zero power of ANY number is 1.

5. Start with rule 1 and let n be -m. We therefore get %28a%5Em%29%28a%5E%28-m%29%29+=+a%5E%28m-m%29.

%28a%5Em%29%28a%5E%28-m%29%29+=+a%5E0
%28a%5Em%29%28a%5E%28-m%29%29+=+1
a%5E%28-m%29+=+1%2F%28a%5Em%29

eg 3%5E%28-2%29 means 1%2F%283%5E2%29


6. Start with rule 3 and let n be 1/m. We therefore get %28a%5Em%29%5E%281%2Fm%29+=+a%5E%28m%2A%281%2Fm%29%29.

%28a%5Em%29%5E%281%2Fm%29+=+a%5E1
%28a%5Em%29%5E%281%2Fm%29+=+a

So, we raise a number "a" to power m and then raise to power 1/m and we get the answer "a".

So, the power 1/m means the "opposite of raising to power m", ie it is the mth root.

eg 25%5E%281%2F2%29 is the square root of 25.
eg 32%5E%281%2F5%29 is the fifth root of 32.

jon