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by tutorphd » Sun Jun 24, 2012 4:44 pm
This is a particular example of the power to power rule: (a^n)^m = a^(n*m).

Powers are shortcut for multiplication and count how many times the base repeats in multiplication.

1000 = 10*10*10 = 10^3 (3 repetitions of the base 10).

In 1000^12, you take these 3 repetitions and multiply by themselves 12 times, ending up with 36 repetitions total of 10. That is why 1000^12 = (10^3)^12 = 10^36.

Your observation is correct, the number of 0s in 1000 shows that it is 10^3.
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