Let * be a binary operation on N, the set of natural numbers, defined by `a*b=` `a^b` for all `a , b in Ndot` Is `'*'` associative or commutative on `N ?`

Explanation

Here, `a**b = a^b` for all `a,b in N`.

Now, `a**b = a^b and b**a = b^a`.

`:. a**b != b**a.`

So, given operation is not associative.

Now, `(a**b)**c = (a^b)**c = (a^b)^c = a^(b^c)`

`a**(b**c) = a**(b^c) = a^(b^c)`

`:. (a**b)**c = a**(b**c).`

Therefore, given operation is commutative on `N`.