**Commutative:**

Consider a, b ∈ N where a * b = a^{b} and b * a = b^{a}

Here, a^{b }and b^{a }are not equal for a, b ∈ N

We know that

a * b ≠ b * a

**Hence, * is not commutative.**

**Associative:**

Consider a, b, c ∈ N

(a * b) * c = a^{b} * c = (a^{b})^{c} = a^{bc}

**In the same way**

a * (b * c) = a * b^{c} = (b)^{ca}

Here, we know that (a * b) * c ≠ a * (b * c)

**Hence, * is not associative.**