AHSME 1970 Problem 13

Given the binary operation $\star$ defined by $a\star b=a^b$ for all positive numbers $a$ and $b$. Then for all positive $a,b,c,n$, we have $\text{(A) } a\star b=b\star a \ \text{(B) } a\star (b\star c)=(a\star b) \star c \\ \text{(C) } (a\star b^n)=(a \star n) \star b \text{(D) } (a\star b)^n =a\star (bn) \\ \text{(E) None of these}$