SOLUTION: Find the positive integer values of a,b and c in 2 to the power of a * 5 to the power of b * c = 1400

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Question 903773: Find the positive integer values of a,b and c in
2 to the power of a * 5 to the power of b * c = 1400
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
2%5Ea%2A5%5Eb%2Ac=1400
We break 1400 down into prime factors:

           1400
           /   \
        100     14
        / \     /\
      10   10  2  7
      /\   /\
     2  5 2  5

1400 = 2%5E3%2A5%5E2%2A7   

2%5Ea%2A5%5Eb%2Ac=2%5E3%2A5%5E2%2A7

So the power of 2 on the left must equal the power of 2
on the right, so a=3.
The power of 5 on the left must equal the power of 5 on
the right, so b=2. And then c=7.

Edwin