15. Let $a$ and $b$ be positive numbers, and satisfy $a^{b}=b^{a}$ and $b=9a$, then the value of $a$ is
(A) 9;
(B) $\frac{1}{3}$;
(C) $\sqrt[9]{9}$;
(D) $\sqrt[3]{3}$;
(E) $\sqrt[4]{3}$.
15. Multiply both sides of $a^{b}=b^{4}$ by $\frac{1}{a}$, and substitute $b=9 a$, we get $a^{8}=9 a$. Since $a \neq 0$, the equation simplifies to $a^{8}=9$. Therefore, $a=9^{\frac{1}{8}}=\left(3^{2}\right)^{\frac{1}{8}}=3^{\frac{1}{4}}$.
(E) True.