You just check. 2^3=8, 3^2=9. Both are not equal. Therefore m^n not equal to n^m.

m + n = n + m [commutative property of addition]

m * n = n * m [commutative property of multiplication]

m(a + b) = ma + mb [distributive property of multiplication]

m^n ≠ n^m

3^2 = 9

2^3 = 8

QED

m^n ≠ n^m

also note that

m/n ≠ n/m

m–n ≠ m–n

All are true apart from the indices which are not interchangeable. eg

3 ^ 2 = 9

2 ^ 3 = 8