A2. The sum of the digits of a five-digit number is 44. What is the product of the digits of this five-digit number?
(A) $2^{3} \cdot 3^{8}$
(B) $2^{3} \cdot 9^{3}$
(C) $8 \cdot 4^{9}$
(D) $8 \cdot 3^{4}$
(E) None of the above.
A2. The sum of 5 one-digit numbers is equal to 44 only if one of these numbers is 8 and the other four numbers are 9, thus $8+9+9+9+9=44$. The product is therefore equal to $8 \cdot 9^{4}=2^{3} \cdot 3^{8}$.