SOLUTION: The ratio (2^2001.3^2003) / (6^2002) is equal to:

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Question 222496: The ratio (2^2001.3^2003) / (6^2002) is equal to:





Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%282%5E2001%2A3%5E2003%29+%2F+%286%5E2002%29
Even if your calculator can handle exponents this large it is highly unlikely that it would be able to display or keep track of all the digits involved. There must be an easier way.

The key is understand exponents and multiplication. The numerator is 2001 2's multiplied by 2003 3's. Using the Commutative and Associative Properties we can rearrange these so that all 2001 2's are paired with 2001 of the 2003 3's. This gives us:
%28%282%2A3%29%5E2001%2A3%2A3%29%2F6%5E2002+=+%286%5E2001%2A3%2A3%29%2F6%5E2002
No we can cancel the 6's. The 2001 6's on top cancel all but one of the 2002 6's on the bottom leaving:
3%2A3%2F6+=+9%2F6+=+3%2F2+=+1%261%2F2