Indices mistakes-3

Algebra Level 4

We know \[a^{mn}=(a^m)(a^m)(a^m)...(a^m)\text{n times}\] But there are some students who claim that \[a^{mn}=(a^m)(a^n)\] Which is obviously incorrect. But not really, since it is true for some triplets of integers,\(a,m,n\). If \(a\in[1,10]\) and \(m,n\in[0,10]\), find the number of possible triplets.

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