SOLUTION: explain why a^0 =1 for any nonzero value of a.

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Question 118664: explain why a^0 =1 for any nonzero value of a.
Found 2 solutions by jim_thompson5910, scott8148:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Remember, when you multiply expressions like and , you simply add the exponents. So

Now when you divide, just undo the multiplication by dividing. In other words,

Now if you divide 2 equal expressions, then you will always get 1 (ie ). So something like

So this shows why for any nonzero value of a. Now I'll let you think this question over: why does "a" have to be nonzero?

Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
when quantities having the same bases are divided, the exponents are subtracted

(2^6)/(2^2)=2^(6-2) ___ (2^6)/(2^2)=2^4 ___ 64/4=16

if the exponents are the same ___ (2^3)/(2^3)=2^(3-3) ___ (2^3)/(2^3)=2^0 ___ 8/8=1

in this case, a=2 ___ a can be any value except for zero (division by zero is undefined)