No. The power 2, which denotes squared, is one of an infinite number of possible values for the index. Indices (or powers) can be negative, fractional, irrational or even complex.
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10,000 is highest HHI because 100 squared= 10,000
The same as pi squared, which is roughly 9.86960440109
(-43)2 = 1,849(same as +43 squared)
No, unless "a" happens to be equal to 0, or to 1.
They mean the same thing. Square meters is the same as meters squared.