A1. Let $a=256$, and $b$ be the product of all positive divisors of $a$. Which of the following equations is correct?
(A) $b=a^{4}$
(B) $b=a^{9}$
(C) $b^{2}=a^{7}$
(D) $b^{2}=a^{9}$
(E) $b^{3}=a^{10}$
A1. Since $a=2^{8}$, we have $b=1 \cdot 2 \cdot 2^{2} \cdot \ldots \cdot 2^{8}=2^{0+1+2+\ldots+8}=2^{36}$. Therefore, $b^{2}=2^{72}=a^{9}$. The correct answer is (D).