AHSME 1961 Problem 9

Let $r$ be the result of doubling both the base and exponent of $a^b$, and $b$ does not equal to $0$. If $r$ equals the product of $a^b$ by $x^b$, then $x$ equals: $\textbf{(A)}\ a \textbf{(B)}\ 2a \textbf{(C)}\ 4a \textbf{(D)}\ 2 \textbf{(E)}\ 4$