Hi stanleyelnats,
Your general approach to this issue is perfect (TESTing VALUES can help to define rules and patterns that you might not immediately recognize), but you have to be clear on the definitions of the 'terms' that you're using.
When you raise an integer to a positive integer exponent, the number of UNIQUE prime factors does NOT change - since you're just multiplying a number by itself a certain number of times, you're not dealing with any 'new' prime numbers (it's just more of the same prime numbers that you already had.
For example
6^1 = 6... and its prime factors are 2 and 3
6^2 = (6)(6).... so its prime factors are still 2 and 3
6^3 = (6)(6)(6).... so its prime factors are still 2 and 3
Etc.
When raising a positive integer to a NEGATIVE integer exponent, you end up with a "fraction under a 1"... but fractions do NOT have prime factors (since they're fractions).
6^(-1) = 1/6.... this is not even an integer, so it has no factors, much less prime factors. Thus, going from "6" to "1/6", we went from 2 prime factors to 0 prime factors.
6^(-2) = 1/36... same issue here though - this is a fraction and it has no factors.
The number 1 is its own unique situation, since 1 has NO prime factors. No matter what power you raise 1 to, you still end up with 1 (so you're still dealing with 0 prime factors).
1^(-1) = 1/1 = 1
1^(-2) = 1/1^2 = 1/1 = 1
1^(-3) = 1/1^3 = 1/1 = 1
Etc.
GMAT assassins aren't born, they're made,
Rich
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