1970 AHSME Problem 13

Given the binary operation \ast defined by a\ast b=a^b for all positive numbers a and b. The for all positive a,b,c,n, we have

\begin{array}{l} \textbf{(A) }a\ast b=b\ast a\qquad \textbf{(B) }a\ast (b\ast c)=(a\ast b)\ast c\qquad\\ \textbf{(C) }(a\ast b^n)=(a\ast n)\ast b\qquad \textbf{(D) }(a\ast b)^n=a\ast (bn)\qquad \textbf{(E) }\text{None of these} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.