Indices mistakes-4

Algebra Level 4

We know \[a^{\frac{m}{n}}=\sqrt[n]{a^m}\] But there are some students who claim that \[a^{\frac{m}{n}}=\frac{a^m}{a^n}\] 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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